Sinmad {VGAM} | R Documentation

## The Singh-Maddala Distribution

### Description

Density, distribution function, quantile function and random generation for the Singh-Maddala distribution with shape parameters `a` and `q`, and scale parameter `scale`.

### Usage

    dsinmad(x, a, scale=1, q.arg, log=FALSE)
    psinmad(q, a, scale=1, q.arg)
    qsinmad(p, a, scale=1, q.arg)
    rsinmad(n, a, scale=1, q.arg)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. If `length(n) > 1`, the length is taken to be the number required.
`a, q.arg` | shape parameters.
`scale` | scale parameter.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### Details

See `sinmad`, which is the VGAM family function for estimating the parameters by maximum likelihood estimation.

### Value

`dsinmad` gives the density, `psinmad` gives the distribution function, `qsinmad` gives the quantile function, and `rsinmad` generates random deviates.

### Note

The Singh-Maddala distribution is a special case of the 4-parameter generalized beta II distribution.

### Author(s)

T. W. Yee

### References

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ: Wiley-Interscience.

### See Also

`sinmad`, `genbetaII`.

### Examples

    y = rsinmad(n=3000, 4, 6, 2)
    fit = vglm(y ~ 1, sinmad(init.a=2.1), trace=TRUE, crit="c")
    coef(fit, mat=TRUE)
    Coef(fit)

[Package VGAM version 0.7-9 Index]