BUM_distribution: Beta-uniform mixture (BUM) distribution

In wyppeter/bbum: BBUM correction for significance testing of p values

Beta-uniform mixture (BUM) distribution

Description

Density and distribution function, and random generation for a BUM distribution. The quantile function cannot be simply expressed and is thus not available.

Usage

dbum(x, lambda, a)

pbum(q, lambda, a)

Arguments

x, q	Vector of quantiles.
lambda	Vector of BUM parameter lambda. lambda is the fraction of null (uniform distribution density) over all density.
a	Vector of BUM parameter a, which corresponds to the a shape parameter of the beta distribution component. It describes the steepness of the beta distribution.

Details

The b parameter of the typical beta distribution function is constrained to be 1 here to limit it to a one-sided, monotonic case, peaking at 0, when 0 < a < 1.

Value

dbum gives the density (PDF), and pbum gives the distribution function (CDF).

Examples

dbum(x = 0.096, lambda = 0.65, a = 0.1)
pbum(q = 0.096, lambda = 0.65, a = 0.1)

dbum(x = c(0.013, 0.04, 0.93, 0.8), lambda = 0.73, a = 0.02)
pbum(q = c(0.013, 0.04, 0.93, 0.8), lambda = 0.73, a = 0.02)

wyppeter/bbum documentation built on Oct. 3, 2023, 3:29 p.m.