Package 'ntsDists'

Balls data

Description

It is related to failure times of 23 bearing balls.

Format

A data.frame with 23 observations of failure times of bearing balls.

Source

Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data, Wiley, Hoboken, NJ, USA.

Salam, S., Khan, Z., Ayed, H., Brahmia, A., Amin, A. (2021). The Neutrosophic Lognormal Model in Lifetime Data Analysis: Properties and Applications, Fuzzy Sets and Their Applications in Mathematics, Article ID 6337759.

Examples

data("balls")
balls

---

Neutrosophic Beta Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Beta distribution with shape parameters shape1 = $\alpha_N$ and shape2 = $\beta_N$.

Usage

dnsBeta(x, shape1, shape2)

pnsBeta(q, shape1, shape2, lower.tail = TRUE)

qnsBeta(p, shape1, shape2)

rnsBeta(n, shape1, shape2)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
shape1	the first shape parameter, which must be a positive interval.
shape2	the second shape parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic beta distribution with parameters $\alpha_N$ and $\beta_N$ has the probability density function

$f_N(x) = \frac{1}{B(\alpha_N, \beta_N)} x^{\alpha_N - 1} (1 - x)^{\beta_N - 1}$

for $\alpha_N \in (\alpha_L, \alpha_U)$, the first shape parameter which must be a positive interval, and $\beta_N \in (\beta_L, \beta_U)$, the second shape parameter which must also be a positive interval, and $0 \le x \le 1$. The function $B(a, b)$ returns the beta function and can be calculated using beta.

Value

dnsBeta gives the density function

pnsBeta gives the distribution function

qnsBeta gives the quantile function

rnsBeta generates random values from the neutrosophic Beta distribution.

References

Sherwani, R. Ah. K., Naeem, M., Aslam, M., Reza, M. A., Abid, M., Abbas, S. (2021). Neutrosophic beta distribution with properties and applications. Neutrosophic Sets and Systems, 41, 209-214.

Examples

dnsBeta(x = c(0.1, 0.2), shape1 = c(1, 1), shape2 = c(2, 2))
dnsBeta(x = 0.1, shape1 = c(1, 1), shape2 = c(2, 2))

x <- matrix(c(0.1, 0.1, 0.2, 0.3, 0.5, 0.5), ncol = 2, byrow = TRUE)
dnsBeta(x, shape1 = c(1, 2), shape2 = c(2, 3))


pnsBeta(q = c(0.1, 0.1), shape1 = c(3, 1), shape2 = c(1, 3), lower.tail = FALSE)
pnsBeta(x, shape1 = c(1, 2), shape2 = c(2, 2))


qnsBeta(p = 0.1, shape1 = c(1, 1), shape2 = c(2, 2))
qnsBeta(p = c(0.25, 0.5, 0.75), shape1 = c(1, 2), shape2 = c(2, 2))

# Simulate 10 numbers
rnsBeta(n = 10, shape1 = c(1, 2), shape2 = c(1, 1))

---

Neutrosophic Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic binomial distribution with parameters size = $n$ and prob = $p_N$.

Usage

dnsBinom(x, size, prob)

pnsBinom(q, size, prob, lower.tail = TRUE)

qnsBinom(p, size, prob)

rnsBinom(n, size, prob)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
size	number of trials (zero or more), which must be a positive interval.
prob	probability of success on each trial, $0 \le prob \le 1$.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic binomial distribution with parameters $n$ and $p_N$ has the density

$f_X(x)=\bigg(\begin{array}{c}n \\ x\end{array}\bigg) p_N^{x}\left(1-p_N\right)^{n-x}$

for $n \in \{1, 2, \ldots\}$ and $p_N \in (p_L, p_U)$ which must be $0<p_N<1$ and $x \in \{0, 1, 2, \ldots, n\}$.

Value

dnsBinom gives the probability mass function

pnsBinom gives the distribution function

qnsBinom gives the quantile function

rnsBinom generates random variables from the Binomial Distribution.

References

Granados, C. (2022). Some discrete neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables. Hacettepe Journal of Mathematics and Statistics, 51(5), 1442-1457.

Examples

# Probability of X = 17 when X follows bin(n = 20, p = [0.9,0.8])
dnsBinom(x = 17, size = 20, prob = c(0.9, 0.8))

x <- matrix(c(15, 15, 17, 18, 19, 19), ncol = 2, byrow = TRUE)
dnsBinom(x = x, size = 20, prob = c(0.8, 0.9))


pnsBinom(q = 17, size = 20, prob = c(0.9, 0.8))
pnsBinom(q = c(17, 18), size = 20, prob = c(0.9, 0.8))
pnsBinom(q = x, size = 20, prob = c(0.9, 0.8))

qnsBinom(p = 0.5, size = 20, prob = c(0.8, 0.9))
qnsBinom(p = c(0.25, 0.5, 0.75), size = 20, prob = c(0.8, 0.9))


# Simulate 10 numbers
rnsBinom(n = 10, size = 20, prob = c(0.8, 0.9))

---

Neutrosophic Discrete Uniform Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic discrete uniform distribution with parameter $k_N$.

Usage

dnsDiscUnif(x, k)

pnsDiscUnif(q, k, lower.tail = TRUE)

qnsDiscUnif(p, k)

rnsDiscUnif(n, k)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
k	parameter of the distribution that must be a positive finite interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

Let $X_N$ be a neutrosophic random variable and denote $X_N \sim \mathcal{DU}(1,2,\ldots,k_N)$ as neutrosophic discrete uniform distribution with parameter $k_N$ has the density

$f_N(x)=\frac{1}{k_N}$

for $k_N \in (k_L, k_U)$.

Value

dnsDiscUnif gives the probability mass function,

pnsDiscUnif gives the distribution function

qnsDiscUnif gives the quantile function

rnsDiscUnif generates random variables from the neutrosophic Discrete Uniform Distribution.

References

Granados, C. (2022). Some discrete neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables. Hacettepe Journal of Mathematics and Statistics, 51(5), 1442-1457.

Examples

dnsDiscUnif(x = 8, k = c(10, 11))
dnsDiscUnif(x = c(8, 9), k = c(10, 11))

pnsDiscUnif(q = 2, k = c(10, 11))

qnsDiscUnif(p = 0.2, k = c(10, 11))


# Simulate 10 numbers
rnsDiscUnif(n = 10, k = c(10, 11))

---

Neutrosophic Exponential Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic exponential distribution with the parameter rate = $\theta_N$.

Usage

dnsExp(x, rate)

pnsExp(q, rate, lower.tail = TRUE)

qnsExp(p, rate)

rnsExp(n, rate)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
rate	the shape parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic exponential distribution with parameter $\theta_N$ has density

$f_N(x)=\theta_N \exp \left(-x \theta_N\right)$

for $x \ge 0$ and $\theta_N \in (\theta_L, \theta_U)$, the rate parameter must be a positive interval and $x \ge 0$.

Value

dnsExp gives the density function

pnsExp gives the distribution function

qnsExp gives the quantile function

rnsExp generates random values from the neutrosophic exponential distribution.

References

Duan, W., Q., Khan, Z., Gulistan, M., Khurshid, A. (2021). Neutrosophic Exponential Distribution: Modeling and Applications for Complex Data Analysis, Complexity, 2021, 1-8.

Examples

# Example 4 of Duan et al. (2021)

data <- matrix(c(4, 4, 3.5, 3.5, 3.9, 4.1, 4.2, 4.2, 4.3, 4.6, 4.7, 4.7),
 nrow = 6, ncol = 2, byrow = TRUE)

dnsExp(data, rate = c(0.23, 0.24))
dnsExp(x = c(4, 4.1), rate = c(0.23, 0.24))

dnsExp(4, rate = c(0.23, 0.23))

# The cumulative distribution function for the nuetrosophic observation (4,4.1)
pnsExp(c(4, 4.1), rate = c(0.23, 0.24), lower.tail = TRUE)

pnsExp(4, rate = c(0.23, 0.24))
# The first percentile
qnsExp(p = 0.1, rate = 0.25)

# The quantiles
qnsExp(p = c(0.25, 0.5, 0.75), rate = c(0.24, 0.25))

# Simulate 10 numbers
rnsExp(n = 10, rate = c(0.23, 0.24))

---

Neutrosophic Gamma Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic gamma distribution with parameter shape = $\alpha_N$ and scale=$\lambda_N$.

Usage

dnsGamma(x, shape, scale)

pnsGamma(q, shape, scale, lower.tail = TRUE)

qnsGamma(p, shape, scale)

rnsGamma(n, shape, scale)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
shape	the shape parameter, which must be a positive interval.
scale	the scale parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic gamma distribution with parameters $\alpha_N$ and $\lambda_N$ has density

$f_N(x)=\frac{1}{\Gamma(\alpha_N) \lambda_N^{\alpha_N}} x^{\alpha_N-1} \exp\{-\left(x / \lambda_N\right)\}$

for $x \ge 0$, $\alpha_N \in (\alpha_L, \alpha_U)$, the shape parameter which must be a positive interval and $\lambda_N \in (\lambda_L, \lambda_U)$, the scale parameter which must be a positive interval. Here, $\Gamma(\cdot)$ is gamma function implemented by gamma.

Value

dnsGamma gives the density function

pnsGamma gives the distribution function

qnsGamma gives the quantile function

rnsGamma generates random variables from the neutrosophic gamma distribution.

References

Khan, Z., Al-Bossly, A., Almazah, M. M. A., and Alduais, F. S. (2021). On statistical development of neutrosophic gamma distribution with applications to complex data analysis, Complexity, 2021, Article ID 3701236.

Examples

data(remission)
dnsGamma(x = remission, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

pnsGamma(q = 20, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

# Calculate quantiles
qnsGamma(p = c(0.25, 0.5, 0.75), shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

# Simulate 10 numbers
rnsGamma(n = 10, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

---

Neutrosophic Generalized Exponential Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic generalized exponential distribution with shape parameter $\delta_N$ and scale parameter $\nu_N$.

Usage

dnsGenExp(x, nu, delta)

pnsGenExp(q, nu, delta, lower.tail = TRUE)

qnsGenExp(p, nu, delta)

rnsGenExp(n, nu, delta)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
nu	the scale parameter, which must be a positive interval.
delta	the shape parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic generalized exponential distribution with parameters $\delta_N$ and $\nu_N$ has density

$f_N(x)=\frac{\delta_N}{\nu_N}\left(1-\exp \left\{-\frac{x_N}{\nu_N}\right\}\right)^{\delta_N-1} \exp\left\{-\frac{x_N}{\nu_N}\right\}$

for $\delta_N \in (\delta_L, \delta_U)$, the shape parameter which must be a positive interval, and $\nu_N \in (\nu_L, \nu_U)$, the scale parameter which must also be a positive interval, and $x \ge 0$.

Value

dnsGenExp gives the density function

pnsGenExp gives the distribution function

qnsGenExp gives the quantile function

rnsGenExp generates random variables from the neutrosophic generalized exponential distribution.

References

Rao, G. S., Norouzirad, M., and Mazarei . D. (2023). Neutrosophic Generalized Exponential Distribution with Application. Neutrosophic Sets and Systems, 55, 471-485.

Examples

data(remission)
dnsGenExp(x = remission, nu = c(7.9506, 8.0568), delta = c(1.2390, 1.2397))

pnsGenExp(q = 20, nu = c(7.9506, 8.0568), delta = c(1.2390, 1.2397))


# Calcluate quantiles
qnsGenExp(c(0.25, 0.5, 0.75), nu = c(7.9506, 8.0568), delta = c(1.2390, 1.2397))

# Simulate 10 values
rnsGenExp(n = 10, nu = c(7.9506, 8.0568), delta = c(1.2390, 1.2397))

---

Neutrosophic Generalized Pareto Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic generalized pareto distribution with parameters shape = $\alpha_N$ and scale=$\beta_N$.

Usage

dnsGenPareto(x, shape, scale)

pnsGenPareto(q, shape, scale, lower.tail = TRUE)

qnsGenPareto(p, shape, scale)

rnsGenPareto(n, shape, scale)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
shape	the shape parameter, which must be a positive interval.
scale	the scale parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic generalized pareto distribution with parameters $\alpha_N$ and $\beta_N$ has density

$f_N(x)=\frac{1}{\beta_N}\left(1+\frac{\alpha_N x_N}{\beta_N} \right)^{-\frac{1}{\alpha_N}-1}$

for $x \ge 0$, $\alpha_N \in (\alpha_L, \alpha_U)$, the shape parameter which must be a positive interval and $\beta_N \in (\beta_L, \beta_U)$, the scale parameter which must be a positive interval.

Value

dnsGenPareto gives the density function

pnsGenPareto gives the distribution function

qnsGenPareto gives the quantile function

rnsGenPareto generates random variables from the neutrosophic generalized pareto distribution.

References

Eassa, N. I., Zaher, H. M., & El-Magd, N. A. A. (2023). Neutrosophic Generalized Pareto Distribution, Mathematics and Statistics, 11(5), 827–833.

Examples

data(remission)
dnsGenPareto(x = remission, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

pnsGenPareto(q = 20, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

# Calculate quantiles
qnsGenPareto(p = c(0.25, 0.5, 0.75), shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

# Simulate 10 numbers
rnsGenPareto(n = 10, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

---

Neutrosophic Generalized Rayleigh Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic generalized Rayleigh distribution with parameters shape = $\nu_N$ and scale = $\sigma_N$.

Usage

dnsGenRayleigh(x, shape, scale)

pnsGenRayleigh(q, shape, scale, lower.tail = TRUE)

qnsGenRayleigh(p, shape, scale)

rnsGenRayleigh(n, shape, scale)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
shape	the shape parameter, which must be a positive interval.
scale	the scale parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic generalized Rayleigh distribution with parameters $\nu_N$ and $\sigma_N$ has the density

$f_N(x)=\frac{2\nu_N}{\sigma_N^2}x \exp\{-\left(\frac{x}{\sigma_N} \right)^2\}\left[1-\exp\{-\left(\frac{x}{\sigma_N} \right)^2\}\right]^{\nu_N-1}$

for $x > 0$, $\nu_N \in (\nu_L, \nu_U)$, the shape parameter which must be a positive interval and $\sigma_N \in (\sigma_L, \sigma_U)$, the scale parameter which must be a positive interval.

Value

dnsGenRayleigh gives the density function

pnsGenRayleigh gives the distribution function

qnsGenRayleigh gives the quantile function

rnsGenRayleigh generates random variables from the Neutrosophic Generalized Rayleigh Distribution.

References

Norouzirad, M., Rao, G. S., & Mazarei, D. (2023). Neutrosophic Generalized Rayleigh Distribution with Application. Neutrosophic Sets and Systems, 58(1), 250-262.

Examples

data(remission)
dnsGenRayleigh(x = remission,shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

pnsGenRayleigh(q = 20, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

# Calculate quantiles
qnsGenRayleigh(p = c(0.25, 0.5, 0.75), shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

# Simulate 10 values
rnsGenRayleigh(n = 10, shape = c(1.1884, 1.1896), scale = c(7.6658, 7.7796))

---

Neutrosophic Geometric Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Geometric distribution with parameter prob = $p_N$.

Usage

dnsGeom(x, prob)

pnsGeom(q, prob, lower.tail = TRUE)

qnsGeom(p, prob)

rnsGeom(n, prob)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
prob	probability of success on each trial, prob$\in (0,1)$.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic Geometric distribution with parameter $p_N$ has the density

$f_X(x)=p_N\left(1-p_N\right)^x$

for $p_N \in (p_L, p_U)$ which must be $0<p_N<1$ and $x \in \{0, 1, 2, \ldots\}$.

Value

dnsGeom gives the probability mass function

pnsGeom gives the distribution function

qnsGeom gives the quantile function

rnsGeom generates random variables from the Geometric Distribution.

References

Granados, C. (2022). Some discrete neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables. Hacettepe Journal of Mathematics and Statistics, 51(5), 1442-1457.

Examples

# One person participates each week with a ticket in a lottery game, where
# the probability of winning the first prize is (10^(-8), 10^(-6)).
# Probability of one persons wins at the fifth year?

dnsGeom(x = 5, prob = c(1e-8, 1e-6))

# Probability of one persons wins after 10 years?
pnsGeom(q = 10, prob = c(1e-8, 1e-6))
pnsGeom(q = 10, prob = c(1e-8, 1e-6), lower.tail = FALSE)
# Calculate the quantiles
qnsGeom(p = c(0.25, 0.5, 0.75), prob = c(1e-8, 1e-6))
# Simulate 10 numbers
rnsGeom(n = 10, prob = c(1e-8, 1e-6))

---

Neutrosophic Kumaraswamy Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Kumaraswamy distribution with shape parameters $\alpha_N$ and $\beta_N$.

Usage

dnsKumaraswamy(x, shape1, shape2)

pnsKumaraswamy(q, shape1, shape2, lower.tail = TRUE)

qnsKumaraswamy(p, shape1, shape2)

rnsKumaraswamy(n, shape1, shape2)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
shape1	the shape parameter, which must be a positive interval.
shape2	the shape parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be genelambdad.

Details

The neutrosophic Kumaraswamy distribution with parameters $\alpha_N$ and $\beta_N$ has density

$f_N(x) = \alpha_N \beta_N x^{\alpha_N-1}(1-x^{\alpha_N})^{\beta_N - 1}$

for $0 \le x \le 1$, $\alpha_N \in (\alpha_L, \alpha_U)$ and $\beta_N \in (\beta_L, \beta_U)$ are shape parameters.

Value

pnsKumaraswamy gives the distribution function

dnsKumaraswamy gives the density

qnsKumaraswamy gives the quantile function

rnsKumaraswamy generates random values from the neutrosophic Kumaraswamy distribution.

References

Ahsan-ul-Haq, M. (2022). Neutrosophic Kumaraswamy Distribution with Engineering Application, Neutrosophic Sets and Systems, 49, 269-276.

Examples

dnsKumaraswamy(x = c(0.5, 0.1), shape1 = c(0.23, 0.24), shape2 = c(1, 2))
dnsKumaraswamy(0.5, shape1 = c(0.23, 0.24), shape2 = c(1, 2))


# The cumulative distribution function for the nuetrosophic observation (4,4.1)
pnsKumaraswamy(q = c(.8, .1), shape1 = c(0.23, 0.24), shape2 = c(1, 2))
# The first percentile
qnsKumaraswamy(p = 0.1, shape1 = 0.24, shape2 = 2)

# The quantiles
qnsKumaraswamy(p = c(0.25, 0.5, 0.75), shape1 = c(0.23, 0.24), shape2 = c(1, 2))

# Simulate 10 numbers
rnsKumaraswamy(n = 10, shape1 = c(0.23, 0.24), shape2 = c(1, 2))

---

Neutrosophic Laplace (Double Exponential) Distribution

Description

Density, distribution function, quantile function, and random generation for the neutrosophic Laplace (Double Exponential) distribution with parameters location = $\theta_N$ and scale = $\beta_N$.

Usage

dnsLaplace(x, location, scale)

pnsLaplace(q, location, scale, lower.tail = TRUE)

qnsLaplace(p, location, scale)

rnsLaplace(n, location, scale)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
location	the location parameter, which is the mean.
scale	the scale parameter, Must consist of positive values.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic Laplace distribution with parameters $\theta_N$ and $\beta_N$ has density

$f_N(x) = \frac{1}{2\beta_N} \exp\left\{-\frac{|x-\theta_N|}{\beta_N}\right\}$

for $-\infty < x < \infty$, $\theta_N \in (\theta_L, \theta_U)$, the location parameter, $\beta_N \in (\beta_L, \beta_U)$, the scale parameter which be a positive interval.

Value

dnsLaplace gives the density function

pnsLaplace gives the distribution function

qnsLaplace gives the quantile function

rnsLaplace generates random values from the neutrosophic Laplace distribution.

References

Rahul, T., Malik, S. C., Raj, M. (2023). Neutrosophic Laplace Distribution with Application in Financial Data Analysis, Neutrosophic Sets and Systems, 57(1), 224-233.

Examples

dnsLaplace(x = c(4, 4.1), location = c(0.23, 0.24), scale = c(1, 2))
dnsLaplace(4, location = c(0.23, 0.24), scale = c(1, 2))


# The cumulative distribution function for the neutrosophic observation (4,4.1)
pnsLaplace(q = c(4, 4.1), location = c(0.23, 0.24), scale = c(1, 2))
# The first percentile
qnsLaplace(p = 0.1, location = 0.24, scale = 2)

# The quantiles
qnsLaplace(p = c(0.25, 0.5, 0.75), location = c(0.23, 0.24), scale = c(1, 2))

# Simulate 10 numbers
rnsLaplace(n = 10, location = c(0.23, 0.24), scale = c(1, 2))

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Neutrosophic Negative Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Negative Binomial distribution with parameters size = $r_N$ and prob = $p_N$.

Usage

dnsNegBinom(x, size, prob)

pnsNegBinom(q, size, prob, lower.tail = TRUE)

qnsNegBinom(p, size, prob)

rnsNegBinom(n, size, prob)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
size	number of trials (zero or more), which must be a positive interval.
prob	probability of success on each trial, $0 < \code{prob} < 1$.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic negative binomial distribution with parameters $r_N$ and $p_N$ has the density

$\left(\begin{array}{c} r_N+x-1 \\ x \end{array}\right) p_N^{r_N}\left(1-p_N\right)^{x}$

for $r_N \in \{1, 2, \ldots\}$ and $p_N \in (p_L, p_U)$ which must be $0<p_N<1$ and $x \in \{0, 1, 2, \ldots\}$.

Value

dnsNegBinom gives the probability mass function

pnsNegBinom gives the distribution function

qnsNegBinom gives the quantile function

rnsNegBinom generates random variables from the Negative Binomial Distribution.

References

Granados, C. (2022). Some discrete neutrosophic distributions with neutrosophic parameters based on neutrosophic random variables. Hacettepe Journal of Mathematics and Statistics, 51(5), 1442-1457.

Examples

dnsNegBinom(x = 1, size = 2, prob = c(0.5, 0.6))
pnsNegBinom(q = 1, size = 2, prob = c(0.5, 0.6))
qnsNegBinom(p = c(0.25, 0.5, 0.75), size = 2, prob = c(0.5, 0.6))
rnsNegBinom(n = 10, size = 2, prob = c(0.6, 0.6))

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Neutrosophic Normal Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic generalized exponential distribution with parameters mean = $\mu_N$ and standard deviation sd = $\sigma_N$.

Usage

dnsNorm(x, mean, sd)

pnsNorm(q, mean, sd, lower.tail = TRUE)

qnsNorm(p, mean, sd)

rnsNorm(n, mean, sd)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
mean	the mean, which must be an interval.
sd	the standard deviations that must be positive.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic normal distribution with parameters mean $\mu_N$ and standard deviation $\sigma_N$ has density function

$f_N(x) = \frac{1}{\sigma_N \sqrt{2 \pi}} \exp\{\left(\frac{\left(X-\mu_N\right)^2}{2 \sigma_N^2}\right)$

} for $\mu_N \in (\mu_L, \mu_U)$, the mean which must be an interval, and $\sigma_N \in (\sigma_L, \sigma_U)$, the standard deviation which must also be a positive interval, and $-\infty < x < \infty$.

Value

dnsNorm gives the density function

pnsNorm gives the distribution function

qnsNorm gives the quantile function

rnsNorm generates random variables from the neutrosophic normal distribution.

References

Patro, S. and Smarandache, F. (2016). The Neutrosophic Statistical Distribution, More Problems, More Solutions. Infinite Study.

Examples

data(balls)
dnsNorm(x = balls, mean = c(72.14087, 72.94087), sd = c(37.44544, 37.29067))

pnsNorm(q = 5, mean = c(72.14087, 72.94087), sd = c(37.44544, 37.29067))

# Calculate quantiles
qnsNorm(p = c(0.25, 0.5, 0.75), mean = c(9.1196, 9.2453), sd = c(10.1397, 10.4577))

# Simulate 10 values
rnsNorm(n = 10, mean = c(4.141, 4.180), sd = c(0.513, 0.521))

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Neutrosophic Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Poisson distribution with parameter $\lambda_N$.

Usage

dnsPois(x, lambda)

pnsPois(q, lambda, lower.tail = TRUE)

qnsPois(p, lambda)

rnsPois(n, lambda)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
lambda	the mean, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic Poisson distribution with parameter $\lambda_N$ has the density

$f_N(x)= \exp\{-\lambda_N\} \frac{\left(\lambda_N\right)^x}{x !}$

for $\lambda_N \in (\lambda_L, \lambda_U)$ which must be a positive interval and $x \in \{0, 1, 2, \ldots\}$.

Value

dnsPois gives the probability mass function

pnsPois gives the distribution function

qnsPois gives the quantile function

rnsPois generates random variables from the neutrosophic Poisson Distribution.

References

Alhabib, R., Ranna, M. M., Farah, H., Salama, A. A. (2018). Some neutrosophic probability distributions. Neutrosophic Sets and Systems, 22, 30-38.

Examples

# In a company, Phone employee receives phone calls, the calls arrive with
# rate of [1 , 3] calls per minute, we will calculate
# the probability that the employee will not receive any call within a minute
dnsPois(x = 0, lambda = c(1, 3))

# the probability that employee would not receive any call within 5 minutes
dnsPois(x = 0, lambda = c(5, 15))
# the probability that the employee will receive at least one call within a minute
pnsPois(q = 1, lambda = c(1, 3), lower.tail = FALSE)
# the probability that the employee will receive at most three calls within 5 minutes
pnsPois(q = 3, lambda = c(5, 15), lower.tail = TRUE)
# Calcaute the quantiles
qnsPois(p = c(0.25, 0.5, 0.75), lambda = c(1, 3))
# Simulate 10 values
rnsPois(n = 10, lambda = 1)

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Neutrosophic Rayleigh Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Rayleigh distribution with parameter $\theta_N$.

Usage

dnsRayleigh(x, theta)

pnsRayleigh(q, theta, lower.tail = TRUE)

qnsRayleigh(p, theta)

rnsRayleigh(n, theta)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
theta	the shape parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic Rayleigh distribution with parameter $\theta_N$ has the density

$f_N(x)=\frac{x}{\theta_N^2} \exp\{-\frac{1}{2}\left(\frac{x}{\theta_N}\right)^2\}$

for $\theta_N \in (\theta_L, \theta_U)$, which must be a positive interval and $x \ge 0$.

Value

dnsRayleigh gives the density function

pnsRayleigh gives the distribution function

qnsRayleigh gives the quantile function

rnsRayleigh generates random variables from the Neutrosophic Rayleigh Distribution.

References

Khan, Z., Gulistan, M., Kausar, N. and Park, C. (2021). Neutrosophic Rayleigh Model With Some Basic Characteristics and Engineering Applications, in IEEE Access, 9, 71277-71283.

Examples

data(remission)
dnsRayleigh(x = remission, theta = c(9.6432, 9.8702))

pnsRayleigh(q = 20, theta = c(9.6432, 9.8702))

# Calculate quantiles
qnsRayleigh(p = c(0.25, 0.5, 0.75), theta = c(9.6432, 9.8702))

# Simulate 10 values
rnsRayleigh(n = 10, theta = c(9.6432, 9.8702))

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Neutrosophic Uniform Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Uniform distribution of a continuous variable $X$ with parameters $a_N$ and $b_N$.

Usage

dnsUnif(x, min, max)

pnsUnif(q, min, max, lower.tail = TRUE)

qnsUnif(p, min, max)

rnsUnif(n, min, max)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
min	lower limits of the distribution. Must be finite.
max	upper limits of the distribution. Must be finite.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic Uniform distribution with parameters $a_N$ and $b_N$ has the density

$f_N(x)=\frac{1}{b_N-a_N}$

for $a_N \in (a_L, a_U)$ lower parameter interval, $b_N \in (b_L,b_U)$, upper parameter interval.

Value

dnsUnif gives the density function

pnsUnif gives the distribution function

qnsUnif gives the quantile function

rnsUnif generates random variables from the neutrosophic Uniform Distribution.

References

Alhabib, R., Ranna, M. M., Farah, H., & Salama, A. A. (2018). Some neutrosophic probability distributions, Neutrosophic Sets and Systems, 22, 30-38.

Examples

dnsUnif(x = 1, min = c(0, 5), max = c(15, 20))
dnsUnif(x = c(6, 10), min = c(0, 5), max = c(15, 20))

punif(q = 1, min = c(0, 5), max = c(15, 20))
punif(q = c(6, 10), min = c(0, 5), max = c(15, 20))

qnsUnif(p = c(0.25, 0.5, 0.75), min = c(0, 5), max = c(15, 20))

rnsUnif(n = 10, min = c(0, 5), max = c(15, 20))

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Neutrosophic Weibull Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Weibull distribution with scale parameter $\alpha_N$ and shape parameter $\beta_N$.

Usage

dnsWeibull(x, shape, scale)

pnsWeibull(q, shape, scale, lower.tail = TRUE)

qnsWeibull(p, shape, scale)

rnsWeibull(n, shape, scale)

Arguments

x	a vector or matrix of observations for which the pdf needs to be computed.
shape	shape parameter, which must be a positive interval.
scale	scale parameter, which must be a positive interval.
q	a vector or matrix of quantiles for which the cdf needs to be computed.
lower.tail	logical; if TRUE (default), probabilities are $P(X \leq x)$; otherwise, $P(X >x)$.
p	a vector or matrix of probabilities for which the quantile needs to be computed.
n	number of random values to be generated.

Details

The neutrosophic Rayleigh distribution with parameters $\alpha_N$ and $\beta_N$ has the density

$f_N(x)=\frac{\beta_N}{\alpha_N^{\beta_N}} x^{\beta_N-1} \exp\{-\left(x / \alpha_N\right)^{\beta_N}\}$

for $\beta_N \in (\beta_L, \beta_U)$ the shape parameter must be a positive interval, $\alpha_N \in (\alpha_L,\alpha_U)$, the scale parameter which be a positive interval, and $x > 0$.

Value

dnsWeibull gives the density function

pnsWeibull gives the distribution function

qnsWeibull gives the quantile function

rnsWeibull generates random variables from the neutrosophic Weibull dDistribution.

References

Alhasan, K. F. H. and Smarandache, F. (2019). Neutrosophic Weibull distribution and Neutrosophic Family Weibull Distribution, Neutrosophic Sets and Systems, 28, 191-199.

Examples

data(remission)
dnsWeibull(x = remission, shape = c(1.0519, 1.0553), scale = c(9.3370, 9.4544))

pnsWeibull(q = 20, shape = c(1.0519, 1.0553), scale = c(9.3370, 9.4544))

# Calculate quantiles
qnsWeibull(p = c(0.25, 0.5, 0.75), shape = c(1.0519, 1.0553), scale = c(9.3370, 9.4544))

# Simulate 10 numbers
rnsWeibull(n = 10, shape = c(1.0519, 1.0553), scale = c(9.3370, 9.4544))

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Remission data

Description

It is related to remission time in months of 128 cancer patients.

Format

A data.frame with 128 observations of remission time in months of cancer patients.

Source

Lee, E.T. and Wang, J. (2003), Statistical Methods for Survival Data Analysis. Vol. 476, John Wiley & Sons,Hoboken, NJ, USA.

Rao, G. S., Norouzirad, M., and Mazarei . D. (2023). Neutrosophic Generalized Exponential Distribution with Application. Neutrosophic Sets and Systems, 55, 471-485.

Examples

data("remission")
remission

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