Theory and Applications of the Unit Gamma/Gompertz Distribution

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models

Study of a Modified Kumaraswamy Distribution

In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on (0,1), called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed

Monitoring the Process Based on Belief Statistic for Neutrosophic Gamma Distributed Product

In this paper, we developed a control chart methodology for the monitoring the mean time between two events using the belief estimator under the neutrosophic gamma distribution. The proposed control chart coefficients and the neutrosophic average run length (NARL) have been determined using different process settings. The performance of the proposed chart is compared with the control chart under classical statistics in terms of NARL using the simulation data and real example. From comparisons, it is concluded that the proposed chart is efficient, effective and adequate to be used under uncertainty environment than the chart under classical statistics

Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications

In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis

Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data

The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the Rényi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of Rényi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given

A New Power Topp–Leone Generated Family of Distributions with Applications

In this paper, we introduce a new general family of distributions obtained by a subtle combination of two well-established families of distributions: the so-called power Topp–Leone-G and inverse exponential-G families. Its definition is centered around an original cumulative distribution function involving exponential and polynomial functions. Some desirable theoretical properties of the new family are discussed in full generality, with comprehensive results on stochastic ordering, quantile function and related measures, general moments and related measures, and the Shannon entropy. Then, a statistical parametric model is constructed from a special member of the family, defined with the use of the inverse Lomax distribution as the baseline distribution. The maximum likelihood method was applied to estimate the unknown model parameters. From the general theory of this method, the asymptotic confidence intervals of these parameters were deduced. A simulation study was conducted to evaluate the numerical behavior of the estimates we obtained. Finally, in order to highlight the practical perspectives of the new family, two real-life data sets were analyzed. All the measures considered are favorable to the new model in comparison to four serious competitors

Determination of the Factors Affecting King Abdul Aziz University Published Articles in ISI by Multilayer Perceptron Artificial Neural Network

Deanship of scientific research established by the King Abdulaziz University provides some research programs for its staff and researchers and encourages them to submit proposals in this regard. Distinct research study (DRS) is one of these programs. It is available all the year and the King Abdulaziz University (KAU) staff can submit more than one proposal at the same time up to three proposals. The rules of the DSR program are simple and easy so it contributes in increasing the international rank of KAU. The authors are offered financial and moral reward after publishing articles from these proposals in Thomson-ISI journals. In this paper, multiplayer perceptron (MLP) artificial neural network (ANN) is employed to determine the factors that have more effect on the number of ISI published articles. The proposed study used real data of the finished projects from 2011 to April 2019

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

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

Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results

Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results