Alpha Logarithm Lomax Distribution with Application

Abstract

    In this paper, we present a new distribution called the Alpha Logarithm Lomax (ALL) distribution by using the Lomax distribution with the alpha Log-G distributions family; the new distribution has three parameters and provides greater flexibility than the Lomax distribution, which is well-known for modeling survival and lifespan data. We investigate several properties of the ALL distribution, including its moment-generating function and various statistical properties, and explore the maximum likelihood estimation (MLE) method to estimate the three parameters of this distribution. We use simulations to demonstrate the effect of MLE, and the new distribution is applied to accurate data to prove its superiority over some other distributions for these data.