Box-Cox Gamma-G Family of Distributions: Theory and Applications

Al-Babtain, Abdulhakim A.; Elbatal, İbrahim; Chesneau, Christophe; Jamal, Farrukh

doi:10.3390/math8101801

Cited by 4 publications

(3 citation statements)

References 41 publications

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“…, u ∈ (0, 1). (9) Thanks to this closed-form expression, we can express several quantile measures, such as SK and KU, as described in Equations ( 7) and ( 8), respectively. Three-dimensional plots of SK and KU are proposed in Figure 2 for a fixed value of β and varying values for α and θ.…”

Section: Tbx Exponential Distributionmentioning

confidence: 99%

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

Bantan

Chesneau

Jamal

et al. 2021

Entropy

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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.

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Section: Tbx Exponential Distributionmentioning

confidence: 99%

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

Bantan

Chesneau

Jamal

et al. 2021

Entropy

Self Cite

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“…Recently, some new family of distributions are proposed by some researchers as type II power Topp-Leone generated family, 28 Sine Topp-Leone-G family, 29 flexible reduced logarithmic-X family 30 and Box-Cox Gamma-G family. 31…”

Section: Introductionmentioning

confidence: 99%

A family of Gamma-generated distributions: Statistical properties and applications

Pourreza

Jamkhaneh

Deiri

2021

Stat Methods Med Res

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In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15

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“…Aslam et al [14] proposed a new family of distributions, namely a modified T-X family of distributions with three most attractive features: flexibility, efficiency and parsimony. The applications of generalized distributions have been discussed with many researchers, and the reader can refer to Gallardo et al [15], Al-Saiary et al [16], Bantan et al [17], Al-Babtain et al [18], and Al-Babtain et al [19]. Yinglin Liu et al [20] proposed a new family of distributions with medical data sets.…”

Section: Introductionmentioning

confidence: 99%

Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

Buzaridah¹,

Ramadan²,

El-Desouky³

2021

OJMSi

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In this paper, a new method for adding parameters to a well-established distribution to obtain more flexible new families of distributions is applied to the inverse Lomax distribution (IFD). This method is known by the flexible reduced logarithmic-X family of distribution (FRL-X). The proposed distribution can be called a flexible reduced logarithmic-inverse Lomax distribution (FRL-IL). The statistical and reliability properties of the proposed models are studied including moments, order statistics, moment generating function, and quantile function. The estimation of the model parameters by maximum likelihood and the observed information matrix are also discussed. In order to assess the potential of the newly created distribution. The extended model is applied to real data and the results are given and compared to other models.

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Box-Cox Gamma-G Family of Distributions: Theory and Applications

Cited by 4 publications

References 41 publications

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

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

A family of Gamma-generated distributions: Statistical properties and applications

Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

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