The Truncated Cauchy Power Family of Distributions with Inference and Applications

Abstract

As a matter of fact, the statistical literature lacks of general family of distributions based on the truncated Cauchy distribution. In this paper, such a family is proposed, called the truncated Cauchy power-G family. It stands out for the originality of the involved functions, its overall simplicity and its desirable properties for modelling purposes. In particular, (i) only one parameter is added to the baseline distribution avoiding the over-parametrization phenomenon, (ii) the related probability functions (cumulative distribution, probability density, hazard rate, and quantile functions) have tractable expressions, and (iii) thanks to the combined action of the arctangent and power functions, the flexible properties of the baseline distribution (symmetry, skewness, kurtosis, etc.) can be really enhanced. These aspects are discussed in detail, with the support of comprehensive numerical and graphical results. Furthermore, important mathematical features of the new family are derived, such as the moments, skewness and kurtosis, two kinds of entropy and order statistics. For the applied side, new models can be created in view of fitting data sets with simple or complex structure. This last point is illustrated by the consideration of the Weibull distribution as baseline, the maximum likelihood method of estimation and two practical data sets wit different skewness properties. The obtained results show that the truncated Cauchy power-G family is very competitive in comparison to other well implanted general families.

Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications

“…The generated new distributions are more flexible in modelling data in practice. Some famous generators families are, Exponentiated -Weibull -generator (Elgarhy et al [2]), the Marshall-Olkin -G family by Marshal and Olkin [3], beta -G family by Eugene et al [4], the generalized odd log logistic -G by Cordeiro et al [5], the generalized transmuted-G by Nofal et al [6], the odd Lindley-G family by Gomes et al [7], a new extended alpha power transformed (APT)-G by Ahmad et al [8], a new APT-G by Elbatal et al [9], a new power Topp-Leone-G by Bantan et al [10], type II general inverse exponential-G by Jamal et al [11], Truncated Inverted Kumaraswamy-G by Bantan et al [12], the exponentiated truncated inverse Weibull-G by Almarashi et al [13], truncated Cauchy power-G by Aldahlan et al [14] and type II power Topp-Leone-G by Bantan et al [15], among others.…”

Sine Topp-Leone-G family of distributions: Theory and applications

“…Motivated by the success of the sine-G family, several trigonometric families have seen the light, with different modeling aims. The most cited are the cos-G family by Souza et al [67,71], sec-G family by Souza et al [67,69], tan-G family by Souza et al [67,68] and Ampadu [15], T-X-tan-G family by Al-Mofleh [10], N sine-G family by Mahmood et al [50], cosine-sine-G family by Chesneau et al [22], arcsine exponentiated-X family by Wenjing et al [73], truncated Cauchy power-G family by Aldahlan et al [12], sine Kumaraswamy-G family by Chesneau and Jamal [23] and TransSC-G family by Jamal and Chesneau [39].…”

The Exponentiated Truncated Inverse Weibull-Generated Family of Distributions with Applications

“…The common scenario consists in truncating the cdf a flexible distribution (inverse or not, generally with support on (0, +∞) or R) over the interval (0, 1) and compounding it by a simple baseline cdf. Current developments include the truncated Fréchet-G (TF-G) family by [17], truncated Burr-G (TB-G) family by [18], truncated Cauchy power-G (TCP-G) family by [19], truncated inverted Kumaraswamy-G (TIK-G) family by [20], and truncated inverse Weibull-G (TIW-G) family, also called type II truncated Fréchet-G (TIITF-G) family, by [21].…”