pmoezipf: Cumulative function.

Description Usage Arguments Details Value See Also Examples

View source: R/pmoezipf.R

Description

Cumulative distribution function for the MOEZipf distribution with parameters α and β.

Usage

1
pmoezipf(x, alpha, beta, log.p = FALSE, lower.tail = TRUE, show.plot = F)

Arguments

x

Vector of positive values.

alpha

Value of the α parameter (α > 1).

beta

Value of the β parameter (β > 0).

log.p

Logical; if TRUE, probabilities p are given as log(p).

lower.tail

Logical; if TRUE (default), probabilities are P[X ≤q x], otherwise, P[X > x].

show.plot

Logical; if TRUE shows the plot of the distibution (default = FALSE).

Details

The cumulative distribution function, F(x), at a given positive real value x, is calcuted from the survival function S(x) as:

F(x) = 1 - S(x),

the survival function S(x) is equal to:

S(x) = \frac{β ζ(α, x + 1)}{ζ(α) - \bar{β}ζ(α, x + 1)}, \forall x > 0

Value

The cumulative probability of each value in vector x.

See Also

smoezipf for the survival probability function.

Examples

1
2
pmoezipf(1:10, 2.5, 1.3)
pmoezipf(1:10, 2.5, 1.3, show.plot = TRUE)

moezipfR documentation built on May 2, 2019, 3:25 a.m.