BUILT-IN MATHEMATICA SYMBOL

LogSeriesDistribution

LogSeriesDistribution[

]
represents a logarithmic series distribution with parameter

.

MORE INFORMATION

LogSeriesDistribution is also known as the logarithmic distribution.

The probability for value in a logarithmic series distribution is for positive integers, and is zero otherwise. »

LogSeriesDistribution allows to be any real number between 0 and 1.

LogSeriesDistribution 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]=

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 the logarithmic series 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:

Limiting values:

Skewness attains its minimum:

Kurtosis:

Limiting values:

Kurtosis attains its minimum:

Different moments with closed forms as functions of parameters:

Moment:

Closed form for symbolic order:

CentralMoment:

FactorialMoment:

Closed form for symbolic order:

Cumulant:

Hazard function:

Quantile function:

Applications (3)

CDF of LogSeriesDistribution is an example of a right-continuous function:

Number of items per order form follows log series distribution with

. Find the probability of at least 3 items per order:

Find most likely number of items per order:

Find the average number of items per order:

The number of accident claims per policy per year from an insurance company:

Since most policies have no accidents or one accident reported, the data may be modelled by a logarithmic series distribution:

Find the probability that there are 2 or more accidents reported for a given policy:

Properties & Relations (1)

The probability of getting any real number except a positive integer is zero:

Possible Issues (2)

LogSeriesDistribution is not defined when

is not strictly between zero and one:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: