## Two well-separated components with positive skewness

#### Source:

This histogram was artificially constructed. The components are in a 2:1 ratio and
both have the same shape.

### Analysis 1:

Fit two gamma components, unconstrained.

#### Remarks:

Gamma distributions give a good fit to the skewed components.

Fitting Gamma components
Proportions and their standard errors
.66765 .33235
.02889 .02889
Means and their standard errors
3.9541 15.9871
.1528 .2020
Sigmas and their standard errors
1.9424 1.8439
.1384 .1549
Degrees of freedom = 21 - 1 + 0 - 0 - 5 - 0 = 15
Chi-squared = 16.4713 (P = .3514)

### Analysis 2:

Fit two normal components, unconstrained.

#### Remarks:

Even though the components are non-normal, and the goodness-of-fit test indicates
a poor fit, the estimates are almost exactly the same as those obtained with gamma
distributions. This is because the components do not overlap; the histogram has
ample information about the proportion, mean and standard deviation of each component.

Fitting Normal components
Proportions and their standard errors
.66658 .33342
.02873 .02873
Means and their standard errors
3.9275 15.9741
.1427 .2013
Sigmas and their standard errors
1.8761 1.8702
.1084 .1497
Degrees of freedom = 21 - 1 + 0 - 0 - 5 - 0 = 15
Chi-squared = 29.2995 (P = .0147)

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