The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data

Abstract

In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.

A New Statistical Model Based on the Novel Generalized Odd Beta Prime Family of Continuous Probability Distributions with Applications to Cancer Disease Data Sets

“…Some families of continuous probability distributions are available in the literature, including the beta generalized-G family by [67], the beta-G by [65], a novel technique for generating families of continuous probability distributions by [68], the Lindley family of distributions by [69], the Zografos-Balakrishnan-G family of distributions by [70], the Topp-Leone family of distributions by [71], the Kumaraswamy transmuted-G family of distributions by [72], and the exponentiated Gompertz generated family of distributions by [73]. Other distribution families that can be cited are the generalized odd half-Cauchy family of distributions by [74], the odd-Burr generalized family of distributions by [75], the extended odd Fréchet-G family of distributions by [76], the generalized odd Weibull generated family of distributions by [77], the generalized odd gamma-G family of distributions by [78], the modified odd Weibull family of distributions by [79], the odd Dagum family of distributions by [80], the Zubair-G family of distributions by [81], the truncated Burr X-G family of distributions by [82], the alpha power Marshall-Olkin-G distributions by [83], the odd log-logistic Burr-X family of distributions by [84], the Teissier-G family of distributions [85], and the generalized alpha exponent power family of distributions by [86] among others.…”

A New Wavelet-Based Privatization Mechanism for Probability Distributions

“…On this topic, we may refer to the so-called “families of probability distributions”, as described in [ 7 , 8 ]. The new probability distributions may be employed efficiently in diverse settings, as described in [ 9 , 10 ]. We may also refer to the work stated in [ 11 ] pointing out the importance of continuous probability distributions in the definition of various measures.…”

Modelling to Engineering Data: Using a New Two-Parameter Lifetime Model

“…Another generator utilizes the shortened random variable. In this context, significant research on the truncated (T)-G families is the T Fréchet-G [1], T Weibull-G [2], Type II T Fréchet-G (TIITFG) [3],T Burr X-G [4], T Lomax-G [5], T power Lo-G (TPLoG) [6], TX family of distributions [7], T log-logistic-G [8], generalized odd Weibull-G [9], Topp-Leone-G [10], transmuted odd Fréchet-G [11] and truncated Cauchy power [12].…”