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

These functions provide the density, cumulative, and random generation
for the mixture of univariate normal distributions with probability
*p*, mean *mu* and standard deviation *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. |

`mu` |
This is a vector of length |

`sigma` |
This is a vector of length |

`lower.tail` |
Logical. This defaults to |

`log,log.p` |
Logical. If |

Application: Continuous Univariate

Density:

*p(theta) = sum p[i] N(mu[i], sigma[i]^2)*Inventor: Unknown

Notation 1:

*theta ~ N(mu, sigma^2)*Notation 2:

*p(theta) = N(theta | mu, sigma^2)*Parameter 1: mean parameters

*mu*Parameter 2: standard deviation parameters

*sigma > 0*Mean:

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

*var(theta) = sum p[i] sigma[i]^(0.5)*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 normal mixture, or Gaussian mixture, distribution is a combination of normal probability distributions.

`dnormm`

gives the density,
`pnormm`

returns the CDF, and
`rnormm`

generates random deviates.

Statisticat, LLC. [email protected]

`ddirichlet`

and
`dnorm`

.

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LaplacesDemon documentation built on July 1, 2018, 9:02 a.m.

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