The Gamma distribution is a continuous distribution bounded at the
lower side. It has three distinct regions. For alpha=1, beta=1/lambda
the Gamma
distribution reduces to the exponential
(lambda) distribution, starting at a
finite value at minimum x and decreasing monotonically thereafter. For
alpha<1, the Gamma distribution tends to infinity at minimum x and
decreases monotonically for increasing x. For alpha>1, the Gamma
distribution is 0 at minimum x, peaks at a value that depends on both
alpha and beta, decreasing monotonically thereafter. If alpha is
restricted to positive integers, the Gamma distribution is reduced to
the Erlang distribution.
Note that the Gamma distribution also reduces to the Chi Squared
distribution for min=0, beta=2, and alpha=nµ/2. It can then be
viewed as
the distribution of the sum of squares of independent unit normal
variables, with nµ degrees of freedom and is used in many
statistical tests.
The Gamma distribution can also be used to approximate the Normal
distribution, for large alpha, while maintaining its strictly positive
values of x [actually (x-min)].
The Gamma distribution has been used to represent lifetimes, lead
times, personal income data, a population about a stable equilibrium,
interarrival times, and service times. In particular, it can represent
lifetime with redundancy.
Examples of each of the regions of the Gamma distribution are shown
above. Note the peak of the distribution moving away from the minimum
value for increasing alpha, but with a much broader distribution.
Gamma distribution in Wikipedia
Samples
Generates a sample of the Gamma distribution.
Name |
Type |
Description |
alpha |
double |
the shape parameter > 0 |
beta |
double |
the scale parameter > 0 |
min |
double |
the minimum x value |
Type |
Description |
double |
the generated sample |
Generates a sample of the Gamma distribution with min set to
0. Is equivalent to gamma(alpha, beta, 0).
Name |
Type |
Description |
alpha |
double |
the shape parameter > 0 |
beta |
double |
the scale parameter > 0 |
Type |
Description |
double |
the generated sample |
Generates a sample of the Gamma distribution using the specified random number generator.
Name |
Type |
Description |
alpha |
double |
the shape parameter > 0 |
beta |
double |
the scale parameter > 0 |
min |
double |
the minimum x value |
r |
java.util.Random |
the random number generator |
Type |
Description |
double |
the generated sample |