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In this article we propose further extension of the generalized Marshall-Olkin-G (G-GMO) family of distribution. The density and survival functions are expressed as infinite mixture of the G-GMO distribution. Asymptotes, Rényi entropy, order statistics, probability weighted moments, moment generating function, quantile function, median, random samp...
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Citations
... Some of these approaches for generated family of distributions are as follows: exponentiated version of the M family in [2], Kumaraswamy Kumaraswamy −G in [3], generalized Kumaraswamy −G in [4], alpha power transformation family in [5], Weibull odd Burr III −G in [6], odd Frechet −G in [7], exponentiated Kumaraswamy −G in [8], type-I half logistic Burr X −G in [9], transmuted Burr X−G in [10], exponentiated generalized −G in [11], gamma Kumaraswamy −G in [12], odd-generalized N-H −G in [13], extended-gamma −G in [14], Kumaraswamy type I half logistic −G in [15], T − X family in [16], gamma −G in [17], Kumaraswamy Poisson −G in [18], exponentiated power-generalized Weibull power series −G in [19], beta generalized Marshall-Olkin Kumaraswamy −G in [20], odd Burr X −G in [21], the Weibull −G in [22], type-II half logistic−G in [23], sec−G in [24], truncated Cauchy power Weibull −G in [25], exponentiated truncated inverse Weibull −G in [26], odd Perks −G in [27], sine Topp-Leone −G in [28], Kumaraswamy generalized Marshall-Olkin −G in [29], a new power Topp-Leone−G in [30], truncated inverted Kumaraswamy −G in [31], transmuted odd Frechet −G in [32], Kumaraswamy Marshal-Olkin −G in [33], Kavya-Manoharan transformation family, [34], among others. Recently, [35], studied the Kumaraswamy (K) generated family of distributions and it has the following cumulative distribution function (CDF) and probability density function (PDF) as below: ...
This paper introduces a new flexible generalized family of distributions, named Kumarswamy Truncated Lomax Distribution. We study its statistical properties including quantile function, skewness, kurtosis, moments, generating functions, incomplete moments and order statistics. Maximum likelihood estimation of the model parameters is investigated. An application is carried out on real data set to illustrate the performance and flexibility of the proposed model.
... They are ideally suited for the prediction and forecasting of real-world issue modeling. There are several ways for generalizing distributions, including: beta-G [1]; generalized Kumaraswamy-G [2]; Weibull odd Burr III-G [3]; Gompertz-G [4]; a new power Topp-Leone-G [5]; exponentiated Kumaraswamy-G [6]; type I half logistic Weibull-G [7]; type I half logistic Burr X-G [8]; the transmuted Burr X-G in [9]; odd power Lindley-G [10]; gamma Kumaraswamy-G [11]; new extended cosine-G in [12]; extended-gamma-G [13]; odd Chen-G [14]; Kumaraswamy type I half logistic-G [15]; log-logistic-G [16]; gamma-G [17]; Kumaraswamy Poisson-G [18]; Kumaraswamy Kumaraswamy-G [19]; additive odd-G [20]; beta generalized Marshall-Olkin Kumaraswamy-G [21]; extended alpha power transformed family of distributions [22]; odd Burr X-G [23]; the Weibull−G in [24]; type II half logistic-G [25]; sec-G [26]; generalized odd linear exponential-G [27]; Stacy-G [28]; odd Perks-G [29]; sine Topp-Leone-G [30]; Kumaraswamy generalized Marshall-Olkin-G [31]; arcsine-exponentiated-X family-G [32]; odd exponentiated half logistic-G [33]; Kumaraswamy Marshall-Olkin-G [34]; and sineexponentiated Weibull−H [35], among others. Recently, ref. [36] proposed the type I half logistic (HL)-G, and it has the next cumulative distribution function (CDF): ...
In this paper, we present the half logistic inverted Nadarajah–Haghigh (HL-INH) distribution, a novel extension of the inverted Nadarajah–Haghigh (INH) distribution. The probability density function (PDF) for the HL-INH distribution might have a unimodal, right skewness, or heavy-tailed shape for numerous parameter values; however, the shape forms of the hazard rate function (HRF) for the HL-INH distribution may be decreasing. Four specific entropy measurements were investigated. Some useful expansions for the HL-INH distribution were investigated. Several statistical and computational features of the HL-INH distribution were calculated. Using simple (SRS) and ranked set sampling (RSS), the parameters for the HL-INH distribution were estimated using the maximum likelihood (ML) technique. A simulation analysis was executed in order to determine the model parameters of the HL-INH distribution using the SRS and RSS methods, and RSS was shown to be more efficient than SRS. We demonstrate that the HL-INH distribution is more adaptable than the INH distribution and other statistical distributions when utilizing three real-world datasets.
... The data were extracted from the following internet link: https://www.worldometers.info/coronavirus/country/uk/ accessed on 3 September 2022: 1, 1, 1, 4, 2, 1, 18, 14, 22, 15, 33, 42, 32, 54, 24, 67, 75,79,75,34,14,89,87,102,78,40,31,21,51,99,40,48,35,19,11,53,57,32,34,17,9,8,46,26,23,27,9,11,10,25,17,9,32,15,8,3,21,34,2,18,13,5, 1, 18, 14, 18, Table 9. Estimated log-likelihood value, model selection criteria, and goodness-of-fit measures of the considered models for the second data set. ...
Citation: Abbas, S.; Muhammad, M.; Jamal, F.; Chesneau, C.; Muhammad, I.; Bouchane, M. A New Extension of the Kumaraswamy Generated Family of Distributions with Applications to Real Data. Computation 2023, 11, 26. Abstract: In this paper, we develop the new extended Kumaraswamy generated (NEKwG) family of distributions. It aims to improve the modeling capability of the standard Kumaraswamy family by using a one-parameter exponential-logarithmic transformation. Mathematical developments of the NEKwG family are provided, such as the probability density function series representation, moments, information measure, and order statistics, along with asymptotic distribution results. Two special distributions are highlighted and discussed, namely, the new extended Kumaraswamy uniform (NEKwU) and the new extended Kumaraswamy exponential (NEKwE) distributions. They differ in support, but both have the features to generate models that accommodate versatile skewed data and non-monotone failure rates. We employ maximum likelihood, least-squares estimation, and Bayes estimation methods for parameter estimation. The performance of these methods is discussed using simulation studies. Finally, two real data applications are used to show the flexibility and importance of the NEKwU and NEKwE models in practice.
... The main objective of generalizing distributions is to induct shape parameter (s) to the parent (or baseline) distributions. The odd Log-Logistic Poisson-G family [3], Kumaraswamy-G Poisson family [31], Dagum-Poisson distribution [8], Poisson-G family [2], Marshall-Olkin Kumaraswamy-G family by Handique et al. [22], Generalized Marshall-Olkin Kumaraswamy-G family by Chakraborty and Handique [9], Exponentiated generalized-G Poisson family [14], Beta-G Poisson family [15], Beta Kumaraswamy-G family [23], Beta generated Kumaraswamy Marshall-Olkin-G family [20], Beta generalized Marshall-Olkin Kumaraswamy-G family [21], Beta generated Marshall-Olkin-Kumaraswamy-G family [11], exponentiated generalized Marshall-Olkin-G family [24], Kumaraswamy generalized Marshall-Olkin-G family [10], Odd moment exponential-G family [25], Odd Burr-G family [6], Generalized transmuted Poisson-G family [18], Weibull-G Poisson family [19], Transmuted transmuted-G family [27], Complementary generalized transmuted Poisson-G family [4] and Marshall Olkin generalized-G Poisson family [30] are some of the notable recent contributions among others. The present proposal is related to Kumaraswamy-G (Kw-G) and Poisson-G families, which we briefly present in the next subsection. ...
In this paper, a new family of lifetime distribution named as the Kumaraswamy Poisson-G distribution is proposed. This model is obtained by mixing the distribution of the minimum of a random number of independent identically Kumaraswamy-G distributed random variables and zero truncated Poisson random variable. The density and survival function are expressed as infinite linear mixture of the Poisson-G distribution. Some mathematical and statistical properties such as quantile function, skewness, kurtosis, probability weighted moments, moment generating function, entropy and asymptotes are investigated. Numerical computation of moments, skewness, kurtosis and entropy are tabulated for a particular distribution of the family with select parameter values. Parameter estimation by methods of maximum likelihood is discussed. Extensive simulation study is carried out under varying sample size to assess the performance of the estimation. A selected distribution from the proposed family is compared with some recently proposed ones by considering two failure time data fitting applications to justify the suitability of the proposed models.
... Using equation (9) in equation (4), for distribution using the results of Section 2.1. For example using equation (12) it can be seen that ...
Unifying the generalized Marshall-Olkin (GMO) and Poisson-G (P-G) a new family of distribution is proposed. Density and the survival function are expressed as infinite mixtures of P-G family. The quantile function, asymptotes, shapes, stochastic ordering, moment generating function, order statistics, probability weighted moments and Rényi entropy are derived. Maximum likelihood estimation with large sample properties is presented. A Monte Carlo simulation is used to examine the pattern of the bias and the mean square error of the maximum likelihood estimators. An illustration of comparison with some of the important sub models of the family in modeling a real data reveals the utility of the proposed family.
... The generated families are generalized and extended most of the classical distributions. Some well-established generators and other recently are the following; the betagenerated ( Eugene et al. (2002)), Kumaraswamy generalized (Cordeiro and de Castro (2011)), gamma-G ( Ristic and Balakrishnan (2012)), Transformed-Transformer ( Alzaatreh et al. (2013)), exponentiated generalized ( Cordeiro et al. (2013)), Weibull-G ( Bourguignon et al. (2014)), Kumaraswamy transmuted-G ( Afify et al. (2016), Type I half-logistic-G ( Cordeiro et al. (2016)), Garhy-G ( Elgarhy et al. (2016)), Kumaraswamy Weibull-G ( Hassan and Elgarhy (2016a)), exponentiated Weibull-G ( Hassan and Elgarhy (2016b)), additive Weibull-G ( Hassan and Hemeda (2016)), Topp-Leone-G ( Al-Shomrani et al. (2016)), exponentiated extended-G ( Elgarhy et al. (2017)), Type II half logistic-G ( Hassan et al. (2017a)), generalized additive Weibull-G ( Hassan et al. (2017b)), alph power transformed-G ( Mahdavi and Kundu (2017)), transmuated Topp-Leone-G ( Yousof et al. (2017)), Kumaraswamy generalized Marshall-Olkin-G ( Chakraborty and Handique (2018)), inverse Weibull-G ( Hassan and Nassr (2018)) and power Lindley-G ( Hassan and Nassr (2019)), among others. Ristic and Balakrishnan (2012) proposed a gamma generator for any continuous distribution G(x) with the following cdf log ( ; ) 1 ...
The Topp-Leone distribution is an attractive model for life testing and reliability studies as it possess a bathtub shaped hazard function. In this paper, we introduce a new family of distributions, depending on Topp–Leone random variable as a generator, called the Type II generalized Topp–Leone–Generated (TIIGTL-G) family. Its density function can be symmetrical, unimodel, left-skewed, right-skewed, and reversed-J shaped, and has increasing, decreasing, upside-down bathtub, J and reversed-J hazard rates. Some special models are presented. Some of its mathematical properties are studied. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters. The importance of one special model; namely; the Type II generalized Topp–Leone exponential is illustrated through two real data sets.
... In recent years, many different methods of generating new continuous distributions by adding one or more parameters to the classical ones were developed and some new families of distributions have been introduced in the statistical literature. The Marshall-Olkin generated family by Marshall and Olkin [16], exponentiated generalized class of distribution studied by Cordeiro et al. [4], exponentiated Marshall-Olkin-G family Dias et al. [7], exponentiated generalized Half-logistic distribution by Thiago et al. [22], Marshall-Olkin Kumaraswamy-G family by Handique et al. [12], Kumaraswamy Marshall-Olkin-G family Alizadeh et al. [2], Kumaraswamy generalized Marshall-Olkin-G family by Chakraborty and Handique [6], generalized Marshall-Olkin Kumaraswamy-G family by Chakraborty and Handique [5], beta Marshall-Olkin-G family by Alizadeh et al. [3], beta generalized Marshall-Olkin-G family by Handique and Chakraborty [9], beta generated Kumaraswamy-G family by Handique et al. [13], beta generated Kumaraswamy Marshall-Olkin-G by Handique and Chakraborty [10] and beta generalized Marshall-Olkin Kumaraswamy-G by Handique and Chakraborty [11] are some of the notable ones among others. ...
... Equations (6) and (8) reveal that the cdf and pdf of EGMO-G(a, b, α, η) are linear combination of corresponding functions of exponentiated-MO-G(α, η). ...
A new generator of continuous distributions called Exponentiated Generalized Marshall–Olkin-G family with three additional parameters is proposed. This family of distribution contains several known distributions as sub models. The probability density function and cumulative distribution function are expressed as infinite mixture of the Marshall–Olkin distribution. Important properties like quantile function, order statistics, moment generating function, probability weighted moments, entropy and shapes are investigated. The maximum likelihood method to estimate model parameters is presented. A simulation result to assess the performance of the maximum likelihood estimation is briefly discussed. A distribution from this family is compared with two sub models and some recently introduced lifetime models by considering three real life data fitting applications.
In this article, we introduce a new generalization of Kavya-Manoharan Burr X (KMBx) distribution called exponentiated KMBx (EKMBx) distribution. The EKMBx distribution has three parameters, one scale and two shapes. These parameters make it very flexible. The EKMBx distribution contains three sub-models. Some basic statistical features like; the quantile function, skewness, kurtosis, moments, incomplete moments and generating functions are derived. The maximum likelihood approach is employed to estimate the parameters of the EKMBx model. The flexibility and applicability of the EKMBx model are demonstrated utilizing two different real-world datasets related to medical science.
Poisson-G family is extended to propose beta Poisson-G family of distribution. Useful expansions of the probability density function and the cumulative distribution function of the proposed family are derived as infinite mixtures of the Poisson-G distribution. Moment generating function, power moments, entropy, quantile function, skewness and kurtosis are investigated. Illustrative numerical computation of moments, skewness, kurtosis and entropy are tabulated for select parameter values. Estimation of model parameters by methods of maximum likelihood is discussed. A simulation experiment is carried out under varying sample size to assess the performance of estimation. Finally, suitability check of the proposed model in comparison to a few recently introduced ones is carried out by considering two life time data sets modeling. ______________________________
In this article, an extension of the transmuted-G family is proposed, in the so-called Poison transmuted-G family of distributions. Some of its statistical properties including quantile function, moment generating function, order statistics, probability weighted moment, stress-strength reliability, residual lifetime, reversed residual lifetime, Rényi entropy and mean deviation are derived. A few important special models of the proposed family are listed. Stochastic characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function, are also studied. The family parameters are estimated via the maximum likelihood approach. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators. The advantage of the proposed family in data fitting is illustrated by means of two applications to failure time data sets.
