Neutrosophic Normal {ntsDists}

Neutrosophic Normal Distribution

Description

Density, distribution function, quantile function and random generation for the neutrosophic generalized exponential distribution with parameters mean = \mu_N and standard deviation sd = \sigma_N.

Usage

dnsNorm(x, mean, sd)

pnsNorm(q, mean, sd, lower.tail = TRUE)

qnsNorm(p, mean, sd)

rnsNorm(n, mean, sd)

Arguments

x

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

mean

the mean, which must be an interval.

sd

the standard deviations that must be positive.

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 normal distribution with parameters mean \mu_N and standard deviation \sigma_N has density function

f_N(x) = \frac{1}{\sigma_N \sqrt{2 \pi}} \exp\{\left(\frac{\left(X-\mu_N\right)^2}{2 \sigma_N^2}\right)

} for \mu_N \in (\mu_L, \mu_U), the mean which must be an interval, and \sigma_N \in (\sigma_L, \sigma_U), the standard deviation which must also be a positive interval, and -\infty < x < \infty.

Value

dnsNorm gives the density function

pnsNorm gives the distribution function

qnsNorm gives the quantile function

rnsNorm generates random variables from the neutrosophic normal distribution.

References

Patro, S. and Smarandache, F. (2016). The Neutrosophic Statistical Distribution, More Problems, More Solutions. Infinite Study.

Examples

data(balls)
dnsNorm(x = balls, mean = c(72.14087, 72.94087), sd = c(37.44544, 37.29067))

pnsNorm(q = 5, mean = c(72.14087, 72.94087), sd = c(37.44544, 37.29067))

# Calculate quantiles
qnsNorm(p = c(0.25, 0.5, 0.75), mean = c(9.1196, 9.2453), sd = c(10.1397, 10.4577))

# Simulate 10 values
rnsNorm(n = 10, mean = c(4.141, 4.180), sd = c(0.513, 0.521))