Neutrosophic Gamma {ntsDists}

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))