Neutrosophic Beta {ntsDists}

Neutrosophic Beta Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Beta distribution with shape parameters shape1 = \alpha_N and shape2 = \beta_N.

Usage

dnsBeta(x, shape1, shape2)

pnsBeta(q, shape1, shape2, lower.tail = TRUE)

qnsBeta(p, shape1, shape2)

rnsBeta(n, shape1, shape2)

Arguments

x

a vector or matrix of observations for which the pdf needs to be computed.

shape1

the first shape parameter, which must be a positive interval.

shape2

the second shape 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 beta distribution with parameters \alpha_N and \beta_N has the probability density function

f_N(x) = \frac{1}{B(\alpha_N, \beta_N)} x^{\alpha_N - 1} (1 - x)^{\beta_N - 1}

for \alpha_N \in (\alpha_L, \alpha_U), the first shape parameter which must be a positive interval, and \beta_N \in (\beta_L, \beta_U), the second shape parameter which must also be a positive interval, and 0 \le x \le 1. The function B(a, b) returns the beta function and can be calculated using beta.

Value

dnsBeta gives the density function

pnsBeta gives the distribution function

qnsBeta gives the quantile function

rnsBeta generates random values from the neutrosophic Beta distribution.

References

Sherwani, R. Ah. K., Naeem, M., Aslam, M., Reza, M. A., Abid, M., Abbas, S. (2021). Neutrosophic beta distribution with properties and applications. Neutrosophic Sets and Systems, 41, 209-214.

Examples

dnsBeta(x = c(0.1, 0.2), shape1 = c(1, 1), shape2 = c(2, 2))
dnsBeta(x = 0.1, shape1 = c(1, 1), shape2 = c(2, 2))

x <- matrix(c(0.1, 0.1, 0.2, 0.3, 0.5, 0.5), ncol = 2, byrow = TRUE)
dnsBeta(x, shape1 = c(1, 2), shape2 = c(2, 3))


pnsBeta(q = c(0.1, 0.1), shape1 = c(3, 1), shape2 = c(1, 3), lower.tail = FALSE)
pnsBeta(x, shape1 = c(1, 2), shape2 = c(2, 2))


qnsBeta(p = 0.1, shape1 = c(1, 1), shape2 = c(2, 2))
qnsBeta(p = c(0.25, 0.5, 0.75), shape1 = c(1, 2), shape2 = c(2, 2))

# Simulate 10 numbers
rnsBeta(n = 10, shape1 = c(1, 2), shape2 = c(1, 1))