Neutrosophic Poisson {ntsDists}

Neutrosophic Poisson Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic Poisson distribution with parameter \lambda_N.

Usage

dnsPois(x, lambda)

pnsPois(q, lambda, lower.tail = TRUE)

qnsPois(p, lambda)

rnsPois(n, lambda)

Arguments

x

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

lambda

the mean, 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 Poisson distribution with parameter \lambda_N has the density

f_N(x)= \exp\{-\lambda_N\} \frac{\left(\lambda_N\right)^x}{x !}

for \lambda_N \in (\lambda_L, \lambda_U) which must be a positive interval and x \in \{0, 1, 2, \ldots\}.

Value

dnsPois gives the probability mass function

pnsPois gives the distribution function

qnsPois gives the quantile function

rnsPois generates random variables from the neutrosophic Poisson Distribution.

References

Alhabib, R., Ranna, M. M., Farah, H., Salama, A. A. (2018). Some neutrosophic probability distributions. Neutrosophic Sets and Systems, 22, 30-38.

Examples

# In a company, Phone employee receives phone calls, the calls arrive with
# rate of [1 , 3] calls per minute, we will calculate
# the probability that the employee will not receive any call within a minute
dnsPois(x = 0, lambda = c(1, 3))

# the probability that employee would not receive any call within 5 minutes
dnsPois(x = 0, lambda = c(5, 15))
# the probability that the employee will receive at least one call within a minute
pnsPois(q = 1, lambda = c(1, 3), lower.tail = FALSE)
# the probability that the employee will receive at most three calls within 5 minutes
pnsPois(q = 3, lambda = c(5, 15), lower.tail = TRUE)
# Calcaute the quantiles
qnsPois(p = c(0.25, 0.5, 0.75), lambda = c(1, 3))
# Simulate 10 values
rnsPois(n = 10, lambda = 1)