Description Usage Arguments Details Value Author(s) See Also Examples

These functions provide the density, cumulative, and random generation
for the mixture of univariate Laplace distributions with probability
*p*, location *mu* and scale *sigma*.

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`x,q` |
This is vector of values at which the density will be evaluated. |

`p` |
This is a vector of length |

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

`location` |
This is a vector of length |

`scale` |
This is a vector of length |

`log` |
Logical. If |

Application: Continuous Univariate

Density:

*p(theta) = sum p[i] L(mu[i], sigma[i])*Inventor: Unknown

Notation 1:

*theta ~ L(mu, sigma)*Notation 2:

*p(theta) = L(theta | mu, sigma)*Parameter 1: location parameters

*mu*Parameter 2: scale parameters

*sigma > 0*Mean:

*E(theta) = sum p[i] mu[i]*Variance:

Mode:

A mixture distribution is a probability distribution that is a combination of other probability distributions, and each distribution is called a mixture component, or component. A probability (or weight) exists for each component, and these probabilities sum to one. A mixture distribution (though not these functions here in particular) may contain mixture components in which each component is a different probability distribution. Mixture distributions are very flexible, and are often used to represent a complex distribution with an unknown form. When the number of mixture components is unknown, Bayesian inference is the only sensible approach to estimation.

A Laplace mixture distribution is a combination of Laplace probability distributions.

One of many applications of Laplace mixture distributions is the Laplace Mixture Model (LMM).

`dlaplacem`

gives the density,
`plaplacem`

returns the CDF, and
`rlaplacem`

generates random deviates.

Statisticat, LLC. [email protected]

`ddirichlet`

and
`dlaplace`

.

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