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In this work, we present a three-parameter lifetime model named Type-II Topp-Leone Bur XII distribution developed using the Type-II ToppLeone (TIITL-G) family of distributions proposed by Elgarhy et al. (2018) which can be used to model reliability problems, fatigue life studies, and survival data has been studied. The newly developed model is more...
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Citations
... Topp-Leone Daggum distribution [25], new hyperbolic sine-generator [26], type II Topp-Leone Bur XII distribution [27], exponentiated Topp-Leone distribution [28], Kumaraswamy distribution [29] transmuted Kumaraswamy distribution [30], exponentiated Kumaraswamy distribution [31], inverted Kumaraswamy distribution [32], unit-Weibull distribution as an alternative to the Kumaraswamy distribution [33], inflated Kumaraswamy distributions [34], generalized inverted Kumaraswamy distribution [35], bivariate Kumaraswamy distribution [36], Topp-Leone-Marshall-Olkin-G family of distributions [37], type II Topp-Leone generated family of distributions [38], Topp-Leone Gompertz-G family of distributions [39], twosided generalized Topp-Leone (TS-GTL) distributions [40], Marshall-Olkin extended inverted Kumaraswamy distribution [41], Marshall-Olkin Kumaraswamy distribution [42], Kumaraswamy-geometric distribution [43], Kumaraswamy-log-logistic distribution [44], Kumaraswamy Pareto distribution [45], Topp Leone generalized inverted Kumaraswamy distribution [46]. ...
... Understanding the distribution and characteristics of these marks is essential for educators and policymakers in assessing the effectiveness of educational programs and implementing targeted interventions to support student learning. The dataset comprises the following marks: 29,25,50,15,13,27,15,18,7,7,8,19,12,18,5,21,15,86,21,15,14,39,15,14,70,44,6,23,58,19,50,23,11,6,34,18,28,34,12,37,4,60,20,23,40,65,19,31 Delving into the dataset, Table 5 unveils the estimated values derived from this diverse dataset. Furthermore, Table ?? offers a glimpse into the information criteria obtained from various models applied to this dataset. ...
In this research, we introduce a groundbreaking distribution, termed the Modified Alpha Power Transformed Inverse Power Lomax Distribution (MAPT-IPLD), which offers a fresh perspective for modeling intricate datasets. By ingeniously amalgamating the modified alpha power transformation with the inverse power Lomax distribution, we have crafted a versatile and robust distribution family. We conduct a comprehensive examination of the theoretical characteristics of the MAPT-IPLD distribution, encompassing stochastic functions, quantile functions, measures, generic moments, probability-weighted moments, and Rényi entropy. .To showcase the practical utility of the MAPT-IPLD distribution, we apply it to diverse real-world datasets, demonstrating its efficacy in accurately capturing a wide array of phenomena. Through comparative analyses with existing models, we underscore its potential as a versatile tool for various statistical applications.In essence, the Modified Alpha Power Transformed Inverse Power Lomax Distribution represents a pioneering approach to statistical modeling, offering unparalleled flexibility and robust performance across a multitude of domains.
... In addition, the distribution is a solution to any data, which cannot be modeled using symmetric distributions. For these reasons, we find the uses of the "Burr XII Distribution" are great and applicable in several disciplines such as "finance, operations and hydrology applications, reliability, income data, household income, crop prices, insurance risk, travel time, flood levels, and failure data" [3,4]. ...
... Some new, important and specific examples of applications of the "Burr XII Distribution" are: in "modeling the lifetime data with different shapes of the hazard function" [4]; in "runoff amounts at Jug Bridge, Maryland" ( [5]); in "annual salaries of 862 professional baseball players of the Major League Baseball" [3]; and in "survival time of medical field, especially in the remission time of bladder cancer patients" [6,7]. ...
... Some of them are: Polosin, et al., [14] who studied "the reliability of the "Burr XII Distribution", and implemented it in loaded system of transit traffic control". Adebisi and Oyebimpe [4] discussed "the ordinary moments, generating function, incomplete moments, mean deviation, Bonferroni and Lorenz curve, and entropy" (ibid). Abdul Hussein and Al-Mosawi [15] considered the "Bayesian estimation problems of two parameters Burr type XII Distribution based on fuzzy data are considered". ...
For the purpose of modelling the Reliability of Burr XII Distribution, a family of shrinkage estimators is proposed for any parameter of any distribution when a prior guess value (0) of is available from the past. In addition, two sub-models of the shrinkage type estimators for estimating the reliability and parameters of the Burr XII Distribution using two types of shrinkage weight functions with the preliminary test of the hypothesis 0 0 θ θ : H against the alternative H 1 : θ ≠ θ 0 have been proposed and studied. The criteria for studying the properties of two sub-models of the reliability estimators which are the , Bias ratio, Mean Squared Error and Relative Efficiency were derived and computed numerically for each sub-model for the purpose of studying the behavior of the estimators for the Burr XII Distribution because they are complicated and contain many complex functions. The numerical results showed the usefulness of the proposed two sub-models of the reliability estimators of Burr XII Distribution relative to the classical estimators for both of the shrinkage functions when the value of the a priori guess value (0) is close to the true value of. In addition, the comparison between the proposed two sub-models of the shrinkage estimators and with classical estimators was made.
... ated family of distributions [3], Topp-Leone Cauchy family of Distributions [4], generalized Odd gamma-G family of distributions [5], Topp-Leone Modified Weibull model [6], Topp-Leone Lomax (TLLo) distribution [7], Marshall-Olkin Topp Leone-G family of distributions [8], arctan power distribution [9], type II generalized Topp-Leone family of distributions [10], new power Topp-Leone generated family of distributions [3], logistic-uniform distribution [11], gamma-uniform distribution [12], uniform distribution of Heegner points [13], Topp-Leone odd log-logistic family of distributions [14], type II exponentiated Half-Logistic-Topp-Leone-G Power Series Class of Distributions [15], Topp Leone power Lomax distribution [16], exponentiated half logistic-Topp-Leone-G power series class of distributions [17], extended generalized exponential power series distribution [18], new inverted Topp-Leone distribution [19], Kumaraswamy inverted Topp-Leone distribution [1], power Lambert uniform distribution [20], step stress and partially accelerated life testing [21], new power Topp-Leone distribution [22], type II power Topp-Leone Daggum distribution [23], new hyperbolic sine-generator [24], type II Topp-Leone Bur XII distribution [25], exponentiated Topp-Leone distribution [26], Kumaraswamy distribution [27] transmuted Kumaraswamy distribution [28], exponentiated Kumaraswamy distribution [29], inverted Kumaraswamy distribution [30], unit-Weibull distribution as an alternative to the Kumaraswamy distribution [31], inflated Kumaraswamy distributions [32], generalized inverted Kumaraswamy distribution [33], bivariate Kumaraswamy distribution [34], Topp-Leone-Marshall-Olkin-G family of distributions [35], type II Topp-Leone generated family of distributions [36], Topp-Leone Gompertz-G family of distributions [37], twosided generalized Topp-Leone (TS-GTL) distributions [38], Marshall-Olkin extended inverted Kumaraswamy distribution [39], Marshall-Olkin Kumaraswamy distribution [40], Kumaraswamy-geometric distribution [41], Kumaraswamy-log-logistic distribution [42], Kumaraswamy Pareto distribution [43], Topp Leone generalized inverted Kumaraswamy distribution [44]. ...
In this paper, we focused on two families of distributions: the Topp–Leone Kumaraswamy family and a novel proposed family of distributions. Subsequently, we explore their composition, leading to a novel family of distributions exhibiting compelling features for data modeling. Specifically, we examine a special member of this novel family, employing the inverse exponential distribution as the cumulative density function. We establish the mathematical properties, investigate the moments and the stochastic properties, and propose a parameter estimation method based on the maximum likelihood of the new model. To assess the applicability of our model, we gather data related to development indicators in Benin Republic. Additionally, employing competing models, we analyze some real-life data and compare the results to the novel distribution. Model performance is evaluated in terms of fitting observed data, and we conduct an in-depth interpretation of the outcomes. This study makes a significant contribution by introducing a novel family of distributions tailored for modeling development indicators. The findings of this research may have substantial implications for statistical analysis and decision-making in the context of Benin’s economic and social development.
... TL Frèchet distribution is studied by [30]. In the same way, TL modified Weibull distribution is derived by [31], and presents the type II TL Bur XII distribution [32]. They showed that the new distribution is more flexible than other generalizations of the Bur distribution. ...
We proposed in this article a new three-parameter distribution, which is referred as the Topp-Leone exponentiated exponential model is proposed. It is used in modeling claim and risk data applied in actuarial and insurance studies. The probability density function of the suggested distribution can be unimodel and positively skewed. Different distributional and mathematical properties of the TL-EE model were provided. Furthermore, we established a maximum likelihood estimation method for estimating the unknown parameters involved in the model, and some actuarial measures were calculated. Also, the potential of these actuarial statistics were provided via numerical simulation experiments. Finally, two real datasets of insurance losses were analyzed to prove the performance and superiority of the suggested model among all its competitors distributions.
... Indeed, the primary concept revolves around augmenting the fundamental distribution by incorporating one or multiple shape parameters into the basic distribution in order to improve its level of flexibility. We can give the following examples: Poisson-G [1], new power Topp-Leone (TL) generated family of distributions [2], generalized Odd gamma-G family of distributions [3], Topp-Leone-Marshall-Olkin-G family of distributions [4], type II Topp-Leone generated family of distributions [5], Topp-Leone-Gompertz-G family of distributions [6], two-sided generalized Topp and Leone (TS-GTL) distributions [7], Topp-Leone Modified Weibull Model [8], Topp-Leone Lomax (TLLo) distribution [9], Marshall-Olkin-Topp-Leone-G family of distributions [10], type II generalized Topp-Leone family of distribution [11], new power Topp-Leone generated family of distributions [2], logistic-uniform distribution [12], gamma-uniform distribution [13], uniform distribution of Heegner points [14], Topp-Leone odd log-logistic family of distributions [15], type II exponentiated half-logistic-Topp-Leone-G power series class of distributions [16], exponentiated half-logistic-Topp-Leone-G power series class of distributions [17], extended generalized exponential power series distribution [18], new inverted Topp-Leone distribution [19], Kumaraswamy inverted Topp-Leone distribution [20], new power Topp-Leone distribution [21], type II power Topp-Leone Daggum distribution [22], new hyperbolic sine-generator [23], type II Topp-Leone Bur XII distribution [24], exponentiated Topp-Leone distribution [25], Kumaraswamy-Kumaraswamy distribution [26], transmuted Kumaraswamy distribution [27], exponentiated Kumaraswamy distribution [28], inverted Kumaraswamy distribution [29], unit-Weibull distribution as an alternative to the Kumaraswamy distribution [30], inflated Kumaraswamy distributions [31], generalized inverted Kumaraswamy distribution [32], bivariate Kumaraswamy distribution [33], Marshall-Olkin extended inverted Kumaraswamy distribution [34], Marshall-Olkin Kumaraswamy distribution [35], Kumaraswamy-geometric distribution [36], Kumaraswamy-log-logistic distribution [37], Kumaraswamy-Pareto distribution [38], Topp-Leone generalized inverted Kumaraswamy distribution [39], twoparameter family of distributions [40], power Lambert uniform distribution [41], and also other families of distributions having important properties and very used in statistical modeling. Moreover, among the existing distributions that are defined on a unit interval, we have the TL distribution, which has great importance in statistics because of its mathematical properties and especially because of the traceability of its cumulative distribution function (CDF). ...
This article puts forth a novel category of probability distributions obtained from the Topp–Leone distribution, the inverse- K K exponential distribution, and the power functions. To obtain this new family, we used the original cumulative distribution functions. After introducing this new family, we gave the motivations that led us to this end and the basis of the new family obtained, followed by the mathematical properties related to the family. Then, we presented the statistic order, the quantile function, the series expansion, the moments, and the entropy (Shannon, Reiny, and Tsallis), and we estimated the parameters by the maximum likelihood method. Finally, using real data, we presented numerical results through data analysis with a comparison of rival models.
... The BXII distribution's limiting case is the Weibull distribution. Numerous investigations have been conducted to increase the adaptability of the BXII distribution, such as the beta BXII distribution, 24 the beta exponentiated BXII distribution, 25 the MO exponentiated BXII distribution, 26 the flexible Weibull extension-BXII distribution, 27 the MO generalized BXII distribution, 28 the Lindley-BXII power series distribution, 29 the generalized Weibull-Burr XII distribution, 30 the Kumaraswamy exponentiated BXII distribution, 31 Type II Topp-Leone BXII distribution, 32 the Weibull BXII (WBXII) distribution, 33 the Kumaraswamy BXII distribution, 34 the exponentiated exponential BXII distribution, 35 the Garhy-BXII distribution, 36 the Gompertz-modified BXII distribution, 37 the odd exponentiated half-logistic BXII distribution, 38 and the harmonic mixture BXII distribution. 39 Among the various extended forms of the BXII distribution, here, we focus on the WBXII distribution presented in Ref. 33. ...
The focus of this study is a new lifetime distribution with five parameters created by combining the Weibull-Burr XII model and the Marshall-Olkin-G family. The newly suggested model is known as the Marshall-Olkin Weibull-Burr XII (MOWBXII) distribution. The new distribution has the benefit of being able to model different types of data, and it is useful in reliability and lifespan statistics. Several current distributions as well as new distributions are included in the MOWBXII distribution. The MOWBXII density function is represented as a linear combination of Burr XII densities. Some statistical properties of the MOWBXII distribution are discussed. Various techniques for estimating the model's parameters are used. The proposed estimation methods are weighted least squares, maximum likelihood, least squares, and maximum product of spacing methods. The effectiveness of different estimates is evaluated in terms of relative bias and mean squared error of the simulation study. Practical illustrations of the MOWBXII distribution are demonstrated using two real datasets. Furthermore , it is shown that the proposed distribution fits well, and this is claimed by comparing with Burr XII-based distributions and some other distributions by means of some measures of goodness-of-fit.
We define and study the four-parameter logistic Burr XII distribution. It is obtained by inserting the three-parameter Burr XII distribution as the baseline in the logistic-X family and may be a useful alternative method to model income distribution and could be applied to other areas. We illustrate that the new distribution can have decreasing and upside-down-bathtub hazard functions and that its density function is an infinite linear combination of Burr XII densities. Some mathematical properties of the proposed model are determined, such as the quantile function, ordinary and incomplete moments, and generating function. We also obtain the maximum likelihood estimators of the model parameters and perform a Monte Carlo simulation study. Further, we present a parametric regression model based on the introduced distribution as an alternative to the location-scale regression model. The potentiality of the new distribution is illustrated by means of two applications to income data sets.
