Metodo de los momentos

he gamma distribution represents the sum of n exponentially distributed random variables. Both the shape and scale parameters can have non-integer values.

Typically, the gamma distribution isdefined in terms of a scale factor and a shape factor. When used to describe the sum of a series of exponentially distributed variables, the shape factor represents the number of variables and the scalefactor is the mean of the exponential distribution. This is apparent when the profile of an exponential distribution with mean set to one is compared to a gamma distribution with a shape factor ofone and a mean of one.

Special cases of the gamma distribution include:

Exponential

When the shape parameter is set to one, and the scale parameter to the mean interval between events,the gamma distribution simplifies to the exponential.

Chi-Squared

A chi-squared distribution is a gamma distribution in which the shape parameter set to the degrees of freedom dividedby two and the scale parameter set to two.

Erlang

The Erlang distribution is used to model the total interval associated with multiple Poisson events, The shape parameters represents thenumber of events and the scale parameter the average interval between events.

Applications

Applications of the gamma distribution can be broadly put under two headings:

Applicationsbased on intervals between events which derive from it being the sum of one or more exponentially distributed variables. In this form, examples of its use include queuing models, the flow of itemsthrough manufacturing and distribution processes and the load on web servers and the many and varied forms of telecom exchange.

Due to its moderately skewed profile, it can be used as a model in arange of disciplines, including climatology where it is a workable model for rainfall and financial services where it has been used for modelling insurance claims and the size of loan defaults and as...