VGAM (version 1.0-4)

## 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, scale = 1, shape1.a, shape3.q, log = FALSE)
psinmad(q, scale = 1, shape1.a, shape3.q, lower.tail = TRUE, log.p = FALSE)
qsinmad(p, scale = 1, shape1.a, shape3.q, lower.tail = TRUE, log.p = FALSE)
rsinmad(n, scale = 1, shape1.a, shape3.q)```

## 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.

shape1.a, shape3.q

shape parameters.

scale

scale parameter.

log

Logical. If `log = TRUE` then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in `pnorm` or `qnorm`.

## Value

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

## Details

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

## References

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

`sinmad`, `genbetaII`.

## Examples

Run this code
```# NOT RUN {
sdata <- data.frame(y = rsinmad(n = 3000, scale = exp(2),
shape1 = exp(1), shape3 = exp(1)))
fit <- vglm(y ~ 1, sinmad(lss = FALSE, ishape1.a = 2.1), data = sdata,
trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit)
# }
```

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