Neutrosophic Negative Binomial {ntsDists}

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))