mixOnekn function

Two-component Normal Mixture Estimation with One Known Component

`mixOnekn' is used for the estimation of the following two-component mixture model: [REMOVE_ME]$h(x;\boldsymbol{\theta},f) = \pi f(x-\mu_1)+(1-\pi)f(x-\mu_2), [REMOVE_ME_2]$

where $\boldsymbol{\theta}=(\pi,\mu_1,\mu_2)^{\top}$ is the parameter to estimate, $f$ is an unknown density function that is symmetric at zero. The parameters are estimated by assuming $f$ is the normal density and the first component has a mean of 0. This function can be used to obtain initial values for the mixMPHD function.

mixOnekn(x, sigma.known = NULL)

Arguments

• x: a vector of observations.
• sigma.known: standard deviation of the first component (if known). Default is NULL, which calculates the component standard deviations using the given observations x.

Returns

A list containing the following elements: - mu: estimated 2 component means, where the first mean is 0.

• sigma: estimated 2 component standard deviations.

• pi: estimated 2 mixing proportions.

• lik: final likelihood.

Description

`mixOnekn' is used for the estimation of the following two-component mixture model:

where $\boldsymbol{\theta}=(\pi,\mu_1,\mu_2)^{\top}$ is the parameter to estimate, $f$ is an unknown density function that is symmetric at zero. The parameters are estimated by assuming $f$ is the normal density and the first component has a mean of 0. This function can be used to obtain initial values for the mixMPHD function.

Examples

# see examples for the `mixMPHD' function.

See Also

mixMPHD