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The aim of this article is to introduce and study a new extension of Lomax distribution with a four-parameter named as the Marshall–Olkin alpha power Lomax (MOAPL) distribution. Some statistical properties of this distribution are discussed as quantile, median, linear representation, non-central moments, and moment generating function. Maximum likelihood estimation (MLE), maximum product spacing (MPS), and Least Square (LS) method for the MOAPL distribution parameters are discussed. The problem of this article is to describe real-life phenomena by using statistical distributions. For this reason, the theory of statistical distribution and generating new distributions are of great interest. Many authors studied and generated new distributions from old ones. A numerical study using real data analysis and Monte-Carlo simulation is performed to compare different methods of estimation. The superiority of the new model over some well-known distributions is illustrated by physics and economics real data sets. The MOAPL model can produce better fits than some well-known distributions as Marshall–Olkin Lomax, alpha power Lomax, Lomax distribution, Marshall–Olkin alpha power exponential, Kumaraswamy-generalized Lomax, exponentiated Lomax, and power Lomax.

Marshall–Olkin Alpha Power Lomax Distribution: Estimation Methods, Applications on Physics and Economics