Papers by Abdisalam Hassan Muse
Mathematical Problems in Engineering
In the real life, there exists limited information or uncertainty in knowledge about failure and ... more In the real life, there exists limited information or uncertainty in knowledge about failure and repair rates which follow one of the standard distributions as exponential distribution and Weibull distribution with some parameters. We suppose that these parameters are fuzzy which allow one to specify a system design for a “worst-case scenario.” In this paper, the fuzzy availability and the fuzzy reliability of a redundant repairable parallel k-out-of-n warm standby system with common-cause failure are evaluated. We assume that the failure time of each operating unit or warm standby unit follows Weibull distribution with two fuzzy parameters and the repair time of any failed unit follows exponential distribution with one fuzzy parameter. Each fuzzy parameter is represented by triangular membership function estimated from statistical data taken from random samples of each unit. Also, we give a numerical example for a fuzzy repairable parallel 3-out-of-5 warm standby system with two ac...
This scientific report aims to provide a comprehensive understanding of new compound G family of ... more This scientific report aims to provide a comprehensive understanding of new compound G family of probability distributions with copulas, shedding light on their mathematical properties and demonstrating their applicability in various real data settings. The insights from this study can benefit researchers, statisticians, and practitioners in their efforts to model complex dependencies and make informed decisions based on multivariate data analysis. The versatility of compound families of continuous probability distributions makes them useful for modelling a variety of events. They can be used to simulate the distribution of a system's time to failure, the amount of money lost in a financial transaction, or the number of accidents in a particular year, for instance. One of the main advantages of using compound families of continuous probability distributions is that they are flexible. This means that they can be used to model a wide range of phenomena, even those that are not well-described by other distributions. Additionally, compound families of continuous probability distributions are often easy to understand and use. Another advantage of using compound families of continuous probability distributions is that they can be used to model the dependence between two or more random variables. In this work, a novel G family called the generalized Weibull Poisson G family is derived and analyzed. The new compound G family of distributions is derived based on the zero-truncated-Poisson G and the generalized Weibull G families. Its statistical characteristics are mathematically studied. The Clayton copula, Archimedean-Ali-Mikhail-Haq copula, Renyi's entropy copula, copula of Farlie, Gumbel and Morgenstern and its modified version which contains four minor types are used to construct some new bivariate type G families. The Lomax model with one parameter receives special attention. The relevance of the new family is demonstrated through two examples from everyday life.
Scientific Reports, Jul 28, 2023
The paper presents a novel statistical approach for analyzing the daily coronavirus case and fata... more The paper presents a novel statistical approach for analyzing the daily coronavirus case and fatality statistics. The survival discretization method was used to generate a two-parameter discrete distribution. The resulting distribution is referred to as the "Discrete Marshall-Olkin Length Biased Exponential (DMOLBE) distribution". Because of the varied forms of its probability mass and failure rate functions, the DMOLBE distribution is adaptable. We calculated the mean and variance, skewness, kurtosis, dispersion index, hazard and survival functions, and second failure rate function for the suggested distribution. The DI index demonstrates that the proposed model can represent both over-dispersed and under-dispersed data sets. We estimated the parameters of the DMOLBE distribution. The behavior of ML estimates is checked via a comprehensive simulation study. The behavior of Bayesian estimates is checked by generating 10,000 iterations of Markov chain Monte Carlo techniques, plotting the trace, and checking the proposed distribution. From simulation studies, it was observed that the bias and mean square error decreased with an increase in sample size. To show the importance and flexibility of DMOLBE distribution using two data sets about deaths due to coronavirus in China and Pakistan are analyzed. The DMOLBE distribution provides a better fit than some important discrete models namely the discrete Burr-XII, discrete Bilal, discrete Burr-Hatke, discrete Rayleigh distribution, and Poisson distributions. We conclude that the new proposed distribution works well in analyzing these data sets. The data sets used in the paper was collected from 2020 year.
IEEE Access
This paper presents a novel probability distribution, namely the new XLindley distribution, deriv... more This paper presents a novel probability distribution, namely the new XLindley distribution, derived from a unique combination of exponential and gamma distributions through a special mixture formulation. The study extensively investigates the mathematical properties of the proposed distribution, including but not limited to the moment generation function, moments of different orders, mode identification, and the quantile function. Furthermore, the research employs a Monte Carlo simulation to assess and compare the performance of various estimators in estimating the unknown parameter of the new XLindley distribution. These estimators are carefully evaluated and analyzed in terms of their efficiency and accuracy, providing valuable insights into the practical application of the new distribution in statistical modeling and data analysis contexts. The voltage and failure time data in the field of engineering are used to model the proposed distribution. The new model is compared with many current distributions such as Xlindley, gamma, Weibull, exponential, Lindley, Shanker, Akash, Zeghdoudi, Chris-Jerry, and Xgamma. Among all models, it is concluded that the new one-parameter distribution performed the best in modeling based on criteria such as the Akaike information criterion, Bayesian information criterion, and others. The real data results show that the proposed distribution exhibits greater flexibility and improved goodness of fit compared to alternative distributions. The new XLindley distribution could be useful in modeling real-life data and may warrant further exploration in future research. Overall, this study contributes to the field of probability distributions and provides new insights for statistical modeling.
PLOS ONE, Apr 10, 2023
This paper provides a novel model that is more relevant than the well-known conventional distribu... more This paper provides a novel model that is more relevant than the well-known conventional distributions, which stand for the two-parameter distribution of the lifetime modified Kies Topp-Leone (MKTL) model. Compared to the current distributions, the most recent one gives an unusually varied collection of probability functions. The density and hazard rate functions exhibit features, demonstrating that the model is flexible to several kinds of data. Multiple statistical characteristics have been obtained. To estimate the parameters of the MKTL model, we employed various estimation techniques, including maximum likelihood estimators (MLEs) and the Bayesian estimation approach. We compared the traditional reliability function model to the fuzzy reliability function model within the reliability analysis framework. A complete Monte Carlo simulation analysis is conducted to determine the precision of these estimators. The suggested model outperforms competing models in real-world applications and may be chosen as an enhanced model for building a statistical model for the COVID-19 data and other data sets with similar features.
IEEE Access
This work proposes a new extension to the XLindley model called an inverse XLindley distribution ... more This work proposes a new extension to the XLindley model called an inverse XLindley distribution (IXLD). Its probability density function and hazard rate function shapes were deduced mathematically. Several statistical properties of the IXLD were derived mathematically. We use ten different approaches to calculate the parameters of the IXLD. The asymptotic behaviour of these estimators were studied thanks to a comprehensive simulation investigation. Through modelling real data sets, the effectiveness and applicability of the IXLD are examined. This proves that the IXLD better fits the real data set than competing models.
Journal of Mathematics
The purpose of this research is to interpolate bipolarity into the definition of the vague soft s... more The purpose of this research is to interpolate bipolarity into the definition of the vague soft set. This gives a new more applicable, flexible, and generalized extension of the soft set, the fuzzy soft set, or even the vague soft set, which is the bipolar vague soft set. In addition, types of bipolar vague soft sets, as well as some new related concepts and operations are established with examples. Moreover, properties of bipolar vague soft sets including absorption, commutative, associative, distributive, and De Morgan’s laws are discussed in detail. Furthermore, a bipolar vague soft set-designed decision-making algorithm is provided generalizing Roy and Maji method. This allows making more effective decisions to choose the optimal alternative. Finally, an applied problem is introduced with a comparative analysis to illustrate how the proposed algorithm works more successfully than the previous models for problems that contain uncertain ambiguous data.
Journal of Function Spaces
The decision-making technique, launched by Roy and Maji, is considered an effective method to ove... more The decision-making technique, launched by Roy and Maji, is considered an effective method to overcome uncertainty and fuzziness in decision-making problems, though, adapting it to reflect the problem parameters’ vagueness, as well as multibipolarity, is very difficult. So, in this article, the bipolarity is interpolated into the multivague soft set of order n . This gives a new more generalized, flexible, and applicable extension than the fuzzy soft model, or any previous hybrid model, which is the bipolar-valued multivague soft model of dimension n . Moreover, types of bipolar-valued multivague soft sets of dimension n , as well as some new associated concepts and operations, are investigated with examples. Furthermore, properties of bipolar-valued multivague soft sets of dimension n including absorption, commutative, associative, and distributive properties, as well as De Morgan’s laws, are provided in detail. Finally, a bipolar-valued multivague soft set-designed decision-making...
Journal of Mathematics
The constant-stress partially accelerated life test (CSPALT) model with Type-II hybrid censoring ... more The constant-stress partially accelerated life test (CSPALT) model with Type-II hybrid censoring scheme (Type-II HCS) is the subject of our research. Units have a lifetime that follows the generalized Rayleigh distribution. Bayesian and E-Bayesian estimates are derived by applying two of the loss functions, mainly the squared error loss (SEL) and LINEX loss functions. Bayesian and E-Bayesian estimates are obtained using Markov chain Monte Carlo (MCMC) methods. To prove the applicability and the importance of the subject, a test for real data will be provided. To evaluate the distribution’s effectiveness, we utilized a variety of datasets and proposed several kinds of censoring. Finally, all results are compared in order to determine the effectiveness of the proposed methods. All major findings are concluded in the conclusion section.
Mathematical Problems in Engineering, 2022
An extension of the cosine generalized family is presented in this paper by using the cosine trig... more An extension of the cosine generalized family is presented in this paper by using the cosine trigonometric function and method of parameter induction concurrently. Prominent characteristics of the proposed family along with useful results are extracted. Moreover, two new subfamilies and several special models are also deduced. A four-parameter model called an Extended Cosine Weibull (ECW) with its mathematical properties is studied deeply. Graphical study reveals that the new model adopts right- and left-skewed, symmetrical, and reversed-J density shapes, while all possible monotone and nonmonotone shapes are exhibited by the hazard rate function. The maximum likelihood technique is exercised for parametric estimation, while estimation performance is accessed via Monte Carlo simulation study graphically and numerically. The superiority of the presented model over several outstanding and competing models is confirmed via three reliability and survival dataset applications.
Alexandria Engineering Journal, 2022
Complexity, 2021
This paper aims to introduce a superior discrete statistical model for the coronavirus disease 20... more This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and...
Complexity
In several experiments of survival analysis, the cause of death or failure of any subject may be ... more In several experiments of survival analysis, the cause of death or failure of any subject may be characterized by more than one cause. Since the cause of failure may be dependent or independent, in this work, we discuss the competing risk lifetime model under progressive type-II censored where the removal follows a binomial distribution. We consider the Akshaya lifetime failure model under independent causes and the number of subjects removed at every failure time when the removal follows the binomial distribution with known parameters. The classical and Bayesian approaches are used to account for the point and interval estimation procedures for parameters and parametric functions. The Bayes estimate is obtained by using the Markov Chain Monte Carlo (MCMC) method under symmetric and asymmetric loss functions. We apply the Metropolis–Hasting algorithm to generate MCMC samples from the posterior density function. A simulated data set is applied to diagnose the performance of the two t...
Complexity, Dec 10, 2021
e purpose of this paper is to investigate a new family of distributions based on an inverse trigo... more e purpose of this paper is to investigate a new family of distributions based on an inverse trigonometric function known as the arctangent function. In the context of actuarial science, heavy-tailed probability distributions are immensely beneficial and play an important role in modelling data sets. Actuaries are committed to finding for such distributions in order to get an excellent fit to complex economic and actuarial data sets. e current research takes a look at a popular method for generating new distributions which are excellent candidates for dealing with heavy-tailed data. e proposed family of distributions is known as the Arctan-X family of distributions and is introduced using an inverse trigonometric function. For the specific purpose of the show of strength, we studied the Arctan-Weibull distribution as a special case of the developed family. To estimate the parameters of the Arctan-Weibull distribution, the frequentist approach, i.e., maximum likelihood estimation, is used. A rigorous Monte Carlo simulation analysis is used to determine the efficiency of the obtained estimators. e Arctan-Weibull model is demonstrated using a realworld insurance data set. e Arctan-Weibull is compared to well-known two-, three-, and four-parameter competitors. Among the competing distributions are Weibull, Kappa, Burr-XII, and beta-Weibull. For model comparison, we used the most precise tests used to know whether the Arctan-Weibull distribution is more useful than competing models.
Mathematical and Computational Applications
This study aims to propose a flexible, fully parametric hazard-based regression model for censore... more This study aims to propose a flexible, fully parametric hazard-based regression model for censored time-to-event data with crossing survival curves. We call it the accelerated hazard (AH) model. The AH model can be written with or without a baseline distribution for lifetimes. The former assumption results in parametric regression models, whereas the latter results in semi-parametric regression models, which are by far the most commonly used in time-to-event analysis. However, under certain conditions, a parametric hazard-based regression model may produce more efficient estimates than a semi-parametric model. The parametric AH model, on the other hand, is inappropriate when the baseline distribution is exponential because it is constant over time; similarly, when the baseline distribution is the Weibull distribution, the AH model coincides with the accelerated failure time (AFT) and proportional hazard (PH) models. The use of a versatile parametric baseline distribution (generalize...
Axioms
The purpose of this study is to propose a novel, general, tractable, fully parametric class for h... more The purpose of this study is to propose a novel, general, tractable, fully parametric class for hazard-based and odds-based models of survival regression for the analysis of censored lifetime data, named as the “Amoud class (AM)” of models. This generality was attained using a structure resembling the general class of hazard-based regression models, with the addition that the baseline odds function is multiplied by a link function. The class is broad enough to cover a number of widely used models, including the proportional hazard model, the general hazard model, the proportional odds model, the general odds model, the accelerated hazards model, the accelerated odds model, and the accelerated failure time model, as well as combinations of these. The proposed class incorporates the analysis of crossing survival curves. Based on a versatile parametric distribution (generalized log-logistic) for the baseline hazard, we introduced a technique for applying these various hazard-based and ...
Mathematics
In this study, we consider a general, flexible, parametric hazard-based regression model for cens... more In this study, we consider a general, flexible, parametric hazard-based regression model for censored lifetime data with covariates and term it the “general hazard (GH)” regression model. Some well-known models, such as the accelerated failure time (AFT), and the proportional hazard (PH) models, as well as the accelerated hazard (AH) model accounting for crossed survival curves, are sub-classes of this general hazard model. In the proposed class of hazard-based regression models, a covariate’s effect is identified as having two distinct components, namely a relative hazard ratio and a time-scale change on hazard progression. The new approach is more adaptive to modelling lifetime data and could give more accurate survival forecasts. The nested structure that includes the AFT, AH, and PH models in the general hazard model may offer a numerical tool for identifying which of them is most appropriate for a certain dataset. In this study, we propose a method for applying these various pa...
Alexandria Engineering Journal
Typically, the parametric proportional hazard (PH) model is used to examine data on mortality occ... more Typically, the parametric proportional hazard (PH) model is used to examine data on mortality occurrences. Competing risks are prevalent in health information, making it difficult to manage time to event data in clinical investigations. A Bayesian framework is being developed for managing conflicting risk occurrences in clinical data. The objective of this study is to identify the variables that affect patients' odds of surviving peripheral blood stem-cell transplantation, a therapy option for life-threatening blood disorders. In addition, we want to implement a Bayesian model capable of analysing time-to-event data in the context of competing risk. In this research, we analyse failure reasons in the setting of competing risk models using the generalised log-logistic with right-censored scheme. We present competing risks models for censored survival data in the presence of explanatory variables, where each system contains more than one component in series. We assume that each component's survival time follows a generalized log-logistic distribution. We obtain Bayesian estimates of the component's lifetime distribution parameters and regression coefficients. We present a comprehensive Markov chain Monte Carlo (McMC) method to evaluate the estimators' convergence diagnostics. A real-survival data set dealing with stem-cell transplants demonstrated the model's flexibility and advantages.
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Papers by Abdisalam Hassan Muse