# Bhattacharjee: Bhattacharjee distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

Density, distribution function, and random generation for the Bhattacharjee distribution.

## Usage

 ```1 2 3 4 5``` ```dbhatt(x, mu = 0, sigma = 1, a = sigma, log = FALSE) pbhatt(q, mu = 0, sigma = 1, a = sigma, lower.tail = TRUE, log.p = FALSE) rbhatt(n, mu = 0, sigma = 1, a = sigma) ```

## Arguments

 `x, q` vector of quantiles. `mu, sigma, a` location, scale and shape parameters. Scale and shape must be positive. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required.

## Details

If Z ~ Normal(0, 1) and U ~ Uniform(0, 1), then Z+U follows Bhattacharjee distribution.

Probability density function

f(z) = 1/(2*a) * (Φ((x-μ+a)/σ) - Φ((x-μ+a)/σ))

Cumulative distribution function

F(z) = σ/(2*a) * ((x-μ)*Φ((x-μ+a)/σ) - (x-μ)*Φ((x-μ-a)/σ) + φ((x-μ+a)/σ) - φ((x-μ-a)/σ))

## References

Bhattacharjee, G.P., Pandit, S.N.N., and Mohan, R. (1963). Dimensional chains involving rectangular and normal error-distributions. Technometrics, 5, 404-406.

## Examples

 ```1 2 3 4 5 6``` ```x <- rbhatt(1e5, 5, 3, 5) hist(x, 100, freq = FALSE) curve(dbhatt(x, 5, 3, 5), -20, 20, col = "red", add = TRUE) hist(pbhatt(x, 5, 3, 5)) plot(ecdf(x)) curve(pbhatt(x, 5, 3, 5), -20, 20, col = "red", lwd = 2, add = TRUE) ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.