BUILT-IN MATHEMATICA SYMBOL

DavisDistribution

represents a Davis distribution with scale parameter b, shape parameter n, and location parameter

.

MORE INFORMATION

The probability density for value in a Davis distribution is proportional to for .

DavisDistribution allows b to be any positive real number, to be any non-negative real number, and .

DavisDistribution can be used with such functions as Mean, CDF, and RandomVariate.

EXAMPLES

CLOSE ALL

Basic Examples (3)

Probability density function:

Cumulative distribution function:

Mean and variance:

Probability density function:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

In[3]:=

Out[3]=

Cumulative distribution function:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Mean and variance:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Scope (7)

Generate a set of pseudorandom numbers that have Davis distribution:

Compare its histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness depends only on shape parameter n:

Kurtosis depends only on shape parameter n:

Different moments with closed forms as functions of parameters:

Hazard function:

Quantile function:

Applications (2)

DavisDistribution can be used to model incomes:

Adjust part-time to full-time and select nonzero values:

Fit Davis distribution into the data:

Compare the histogram of the data to the PDF of the estimated distribution:

Find average income at a large state university:

Find the probability that a salary is at most $150,000:

Find the probability that a salary is at least $150,000:

Find the median salary:

Simulate the incomes for 100 randomly selected employees of such a university:

BetaPrimeDistribution can be used to model state per capita incomes:

Fit Davis distribution into the data:

Compare the histogram of the data to the PDF of the estimated distribution:

Find average income per capita:

Find states with income close to the average:

Find the median income per capita:

Find states with income close to the median:

Find log-likelihood value:

Compare with the fit using BetaPrimeDistribution:

Compare with the fit using DagumDistribution:

Compare with the fit using LogLogisticDistribution:

Properties & Relations (2)

Parameter influence on the CDF for each

:

Davis distribution is closed under translation and scaling by a positive factor: