Abstract
We introduced and studied a new generalization of the Burr type X distribution. Some of its properties were derived and numerically analyzed. The new density can be “right-skewed” and symmetric with “unimodal” and many “bimodal” shapes. The new failure rate can be “increasing,” “bathtub,” “J-shape,” “decreasing,” “increasing-constant-increasing,” “reversed J-shape,” and “upside-down (reversed U-shape).” The usefulness and flexibility of the new distribution were illustrated by means of four asymmetric bimodal right- and left-heavy tail real lifetime data.
Highlights
Burr [1] introduced twelve different forms of cumulative distribution functions (CDFs) for modeling real data sets
We present a new bimodal version of the Burr type X (BX) model called the odd Burr BX (OBBX) model based on the family from [20], who merged the generalized odd G (OG)
In order to compare the fits of the OBBX distribution with other competing distributions, we consider the Cramér–von Mises (CVM), the Anderson–Darling (AD), and the Kolmogorov–Smirnov (KS) estimation methods
Summary
Burr [1] introduced twelve different forms of cumulative distribution functions (CDFs) for modeling real data sets. We present a new bimodal version of the BX model called the odd Burr BX (OBBX) model based on the family from [20], who merged the generalized odd G (OG). The OBBX model could be chosen as the best model, especially in modeling asymmetric bimodal failure times data and the asymmetric bimodal right-skewed and heavy-tail survival times data as illustrated in Sections 5.1 and 5.3, respectively.
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