Description Usage Arguments Details Value References See Also Examples

These functions provide the density, distribution function, quantile
function, and random generation for the univariate, skew-Laplace
distribution with location parameter *mu*, and two mixture
parameters: *alpha* and *beta*.

1 2 3 4 |

`x, q` |
These are each a vector of quantiles. |

`p` |
This is a vector of probabilities. |

`n` |
This is the number of observations, which must be a positive integer that has length 1. |

`mu` |
This is the location parameter |

`alpha` |
This is a mixture parameter |

`beta` |
This is a mixture parameter |

`log` |
Logical. If |

Application: Continuous Univariate

Density 1:

*p(theta) = (1/(alpha+beta)) exp((theta-mu)/alpha), theta <= mu*Density 2:

*p(theta) = (1/(alpha+beta)) exp((mu-theta)/beta), theta > mu*Inventor: Fieller, et al. (1992)

Notation 1:

*theta ~ SL(mu, alpha, beta)*Notation 2:

*p(theta) = SL(theta | mu, alpha, beta)*Parameter 1: location parameter

*mu*Parameter 2: mixture parameter

*alpha > 0*Parameter 3: mixture parameter

*beta > 0*Mean:

*E(theta) = mu + beta - alpha*Variance:

*var(theta) = alpha^2 + beta^2*Mode:

*mode(theta) = mu*

This is the three-parameter general skew-Laplace distribution, which is
an extension of the two-parameter central skew-Laplace distribution. The
general form allows the mode to be shifted along the real line with
parameter *mu*. In contrast, the central skew-Laplace has mode
zero, and may be reproduced here by setting *mu=0*.

The general skew-Laplace distribution is a mixture of a negative
exponential distribution with mean *beta*, and the negative
of an exponential distribution with mean *alpha*. The
weights of the positive and negative components are proportional to
their means. The distribution is symmetric when
*alpha=beta*, in which case the mean is *mu*.

These functions are similar to those in the `HyperbolicDist`

package.

`dslaplace`

gives the density,
`pslaplace`

gives the distribution function,
`qslaplace`

gives the quantile function, and
`rslaplace`

generates random deviates.

Fieller, N.J., Flenley, E.C., and Olbricht, W. (1992). "Statistics of
Particle Size Data". *Applied Statistics*, 41, p. 127–146.

`dalaplace`

,
`dexp`

,
`dlaplace`

,
`dlaplacep`

, and
`dsdlaplace`

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
library(LaplacesDemon)
x <- dslaplace(1,0,1,1)
x <- pslaplace(1,0,1,1)
x <- qslaplace(0.5,0,1,1)
x <- rslaplace(100,0,1,1)
#Plot Probability Functions
x <- seq(from=0.1, to=3, by=0.01)
plot(x, dslaplace(x,0,1,1), ylim=c(0,1), type="l", main="Probability Function",
ylab="density", col="red")
lines(x, dslaplace(x,0,0.5,2), type="l", col="green")
lines(x, dslaplace(x,0,2,0.5), type="l", col="blue")
legend(1.5, 0.9, expression(paste(mu==0, ", ", alpha==1, ", ", beta==1),
paste(mu==0, ", ", alpha==0.5, ", ", beta==2),
paste(mu==0, ", ", alpha==2, ", ", beta==0.5)),
lty=c(1,1,1), col=c("red","green","blue"))
``` |

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