# LogSeries: Logarithmic series distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

Density, distribution function, quantile function and random generation for the logarithmic series distribution.

## Usage

 ```1 2 3 4 5 6 7``` ```dlgser(x, theta, log = FALSE) plgser(q, theta, lower.tail = TRUE, log.p = FALSE) qlgser(p, theta, lower.tail = TRUE, log.p = FALSE) rlgser(n, theta) ```

## Arguments

 `x, q` vector of quantiles. `theta` vector; concentration parameter; (`0 < theta < 1`). `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]. `p` vector of probabilities. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required.

## Details

Probability mass function

f(x) = (-1/log(1-θ)*θ^x) / x

Cumulative distribution function

F(x) = -1/log(1-θ) * sum((θ^x)/x)

Quantile function and random generation are computed using algorithm described in Krishnamoorthy (2006).

## References

Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC

Forbes, C., Evans, M. Hastings, N., & Peacock, B. (2011). Statistical Distributions. John Wiley & Sons.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```x <- rlgser(1e5, 0.66) xx <- seq(0, 100, by = 1) plot(prop.table(table(x)), type = "h") lines(xx, dlgser(xx, 0.66), col = "red") # Notice: distribution of F(X) is far from uniform: hist(plgser(x, 0.66), 50) xx <- seq(0, 100, by = 0.01) plot(ecdf(x)) lines(xx, plgser(xx, 0.66), col = "red", lwd = 2) ```

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