Neutrosophic Generalized Pareto {ntsDists}

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))