Truncated Inverted Kumaraswamy Generated Family of Distributions with Applications

Abstract

In this article, we introduce a new general family of distributions derived to the truncated inverted Kumaraswamy distribution (on the unit interval), called the truncated inverted Kumaraswamy generated family. Among its qualities, it is characterized with tractable functions, has the ability to enhance the flexibility of a given distribution, and demonstrates nice statistical properties, including competitive fits for various kinds of data. A particular focus is given on a special member of the family defined with the exponential distribution as baseline, offering a new three-parameter lifetime distribution. This new distribution has the advantage of having a hazard rate function allowing monotonically increasing, decreasing, and upside-down bathtub shapes. In full generality, important properties of the new family are determined, with an emphasis on the entropy (Rényi and Shannon entropy). The estimation of the model parameters is established by the maximum likelihood method. A numerical simulation study illustrates the nice performance of the obtained estimates. Two practical data sets are then analyzed. We thus prove the potential of the new model in terms of fitting, with favorable results in comparison to other modern parametric models of the literature.

A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data

“…The second data set (0.1, 0.33, 0.44, 0.56, 0.59, 0.72, 0.74, 0.77, 0.92, 0.93, 0.96, 1, 1, 1.02, 1.05, 1.07, 07, 1.08, 1.08, 1.08, 1.09, 1.12, 1.13, 1.15, 1.16, 1.2, 1.21, 1.22, 1.22, 1.24, 1.3, 1.34, 1.36, 1.39, 1.44, 1.46, 1.53, 1.59, 1.6, 1.63, 1.63, 1.68, 1.71, 1.72, 1.76, 1.83, 1.95, 1.96, 1.97 (1960). Many other real data sets related to failure times can be found in [13][14][15][16][17][18][19][20]. Figure 3 gives the total time test (TTT) plots.…”

The Truncated Cauchy Power Family of Distributions with Inference and Applications

“…By the use of well-known general families of distributions, one can extend the truncated Cauchy distribution in multiple theoretical or applied directions. For instance, one can use the exp-G family proposed by [ 8 ], the Kumaraswamy-G family introduced by [ 9 ], the beta-G family developed by [ 10 ], the Marshall-Olkin-G family proposed by [ 11 ], the Weibull-G family developed by [ 12 , 13 ], the transmuted-G family developed by [ 14 ], the gamma-G family proposed by [ 15 ], the inverse exponential-G family proposed by [ 16 ], the sine-G family introduced by [ 17 ], and the truncated inverted Kumaraswamy-G family proposed by [ 18 ]. The idea behind this general families is to transform or add (one or several) parameters to a baseline distribution in order to improve its global flexibility, with the aim to gain on the fitting of the resulting models.…”

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].…”