Abstract
A new mixture generalized Pareto distribution is introduced. Then, some of its attributes are explored. The maximum likelihood method and expectation maximization (EM) algorithm have been applied to estimate the parameters for complete and right-censored data. In a simulation study, the bias, absolute bias and mean squared error of the maximum likelihood estimator are compared with those related to the EM estimator. The results show that the absolute bias and mean squared error of the EM estimator are smaller than the related values for the maximum likelihood estimator. Finally, to illustrate its usefulness, the model has been applied to describe real data sets.
Highlights
T HE Pareto distribution is a power-law distribution that was originally used to describe wealth distribution
The Pareto model may be applied to situations, where an equilibrium is found in the distribution of "small" to "large" values
We may point to: the sizes of files transferred on the internet network by TCP/IP, which consists of many smaller files and few larger ones; the hard disk drive error rates, which consist of many small error rates and few large ones; the sizes of human settlements, which consist of many small values related to hamlets/villages and few large values related to cities; the oil reserves volumes in oil fields, which consist of many small fields and few large fields and many other examples
Summary
T HE Pareto distribution is a power-law distribution that was originally used to describe wealth distribution. Jayakumar et al [13], Tahir et al [14], Korkmaz et al [15], Elbatal and Aryal [16], and Chananet and Phaphan [17] proposed new distributions based on the Pareto model. We propose a new model based on a mixture of the GP distribution (1). The proposed model extends mixtures of the exponential, gamma, or Pareto distributions and has sufficient flexibility to describe many real situations.
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