Neutrosophic Binomial {ntsDists}

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))