LognormalMixAlt {EnvStats} | R Documentation |

Density, distribution function, quantile function, and random generation
for a mixture of two lognormal distribution with parameters
`mean1`

, `cv1`

, `mean2`

, `cv2`

, and `p.mix`

.

```
dlnormMixAlt(x, mean1 = exp(1/2), cv1 = sqrt(exp(1) - 1),
mean2 = exp(1/2), cv2 = sqrt(exp(1) - 1), p.mix = 0.5)
plnormMixAlt(q, mean1 = exp(1/2), cv1 = sqrt(exp(1) - 1),
mean2 = exp(1/2), cv2 = sqrt(exp(1) - 1), p.mix = 0.5)
qlnormMixAlt(p, mean1 = exp(1/2), cv1 = sqrt(exp(1) - 1),
mean2 = exp(1/2), cv2 = sqrt(exp(1) - 1), p.mix = 0.5)
rlnormMixAlt(n, mean1 = exp(1/2), cv1 = sqrt(exp(1) - 1),
mean2 = exp(1/2), cv2 = sqrt(exp(1) - 1), p.mix = 0.5)
```

`x` |
vector of quantiles. |

`q` |
vector of quantiles. |

`p` |
vector of probabilities between 0 and 1. |

`n` |
sample size. If |

`mean1` |
vector of means of the first lognormal random variable. The default is |

`cv1` |
vector of coefficient of variations of the first lognormal random variable.
The default is |

`mean2` |
vector of means of the second lognormal random variable. The default is |

`cv2` |
vector of coefficient of variations of the second lognormal random variable.
The default is |

`p.mix` |
vector of probabilities between 0 and 1 indicating the mixing proportion.
For |

Let `f(x; \eta, \theta)`

denote the density of a
lognormal random variable with parameters
`mean=`

`\eta`

and `cv=`

`\theta`

. The density, `g`

, of a
lognormal mixture random variable with parameters `mean1=`

`\eta_1`

,
`cv1=`

`\theta_1`

, `mean2=`

`\eta_2`

,
`cv2=`

`\theta_2`

, and `p.mix=`

`p`

is given by:

```
g(x; \eta_1, \theta_1, \eta_2, \theta_2, p) =
(1 - p) f(x; \eta_1, \theta_1) + p f(x; \eta_2, \theta_2)
```

The default values for `mean1`

and `cv1`

correspond to a
lognormal distribution with parameters
`meanlog=0`

and `sdlog=1`

. Similarly for the default values
of `mean2`

and `cv2`

.

`dlnormMixAlt`

gives the density, `plnormMixAlt`

gives the distribution
function, `qlnormMixAlt`

gives the quantile function, and
`rlnormMixAlt`

generates random deviates.

A lognormal mixture distribution is often used to model positive-valued data
that appear to be “contaminated”; that is, most of the values appear to
come from a single lognormal distribution, but a few “outliers” are
apparent. In this case, the value of `mean2`

would be larger than the
value of `mean1`

, and the mixing proportion `p.mix`

would be fairly
close to 0 (e.g., `p.mix=0.1`

).

Steven P. Millard (EnvStats@ProbStatInfo.com)

Gilliom, R.J., and D.R. Helsel. (1986). Estimation of Distributional Parameters
for Censored Trace Level Water Quality Data: 1. Estimation Techniques.
*Water Resources Research* **22**, 135-146.

Johnson, N. L., S. Kotz, and A.W. Kemp. (1992). *Univariate Discrete
Distributions*. Second Edition. John Wiley and Sons, New York, pp.53-54, and
Chapter 8.

Johnson, N. L., S. Kotz, and N. Balakrishnan. (1994).
*Continuous Univariate Distributions, Volume 1*.
Second Edition. John Wiley and Sons, New York.

LognormalAlt, LognormalMix, Lognormal, NormalMix, Probability Distributions and Random Numbers.

```
# Density of a lognormal mixture with parameters mean=2, cv1=3,
# mean2=4, cv2=5, p.mix=0.5, evaluated at 1.5:
dlnormMixAlt(1.5, mean1 = 2, cv1 = 3, mean2 = 4, cv2 = 5, p.mix = 0.5)
#[1] 0.1436045
#----------
# The cdf of a lognormal mixture with parameters mean=2, cv1=3,
# mean2=4, cv2=5, p.mix=0.5, evaluated at 1.5:
plnormMixAlt(1.5, mean1 = 2, cv1 = 3, mean2 = 4, cv2 = 5, p.mix = 0.5)
#[1] 0.6778064
#----------
# The median of a lognormal mixture with parameters mean=2, cv1=3,
# mean2=4, cv2=5, p.mix=0.5:
qlnormMixAlt(0.5, 2, 3, 4, 5, 0.5)
#[1] 0.6978355
#----------
# Random sample of 3 observations from a lognormal mixture with
# parameters mean1=2, cv1=3, mean2=4, cv2=5, p.mix=0.5.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(20)
rlnormMixAlt(3, 2, 3, 4, 5, 0.5)
#[1] 0.70672151 14.43226313 0.05521329
```

[Package *EnvStats* version 2.8.1 Index]