A New Bimodal Distribution for Modeling Asymmetric Bimodal Heavy-Tail Real Lifetime Data

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.

A New Lomax Extension: Properties, Risk Analysis, Censored and Complete Goodness-of-Fit Validation Testing under Left-Skewed Insurance, Reliability and Medical Data

“…Researchers can explore various aspects of risk analysis, such as dependence modeling, copulas, multivariate extensions, and time series modeling, using the Lomax distribution as a building block. For more details, regression models, applications, and real datasets, see Butt and Khalil [14] for a novel skewed bimodal model for modeling the asymmetric heavy-tail bimodal datasets, Reyes et al [15] for a new bimodal exponential extension with some applications in risk theory, and Gómez et al [16] for asymmetric bimodal double-regression modeling. A few plots of the GELX PDF and HRF are shown in Figure 1.…”

An Asymmetric Bimodal Double Regression Model

“…Other practical examples of bimodality in data can be seen in [4][5][6]. In the literature, there are many proposals discussing bimodal distributions; e.g., the works of [7][8][9][10][11][12]. Bimodal data can be fitted by a mixture of two unimodal distributions.…”