Neutrosophic Generalized Rayleigh {ntsDists}

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))