M. Masoom Ali

Ball State University · Department of Mathematical Sciences

We introduce a new class of continuous distributions called the generalized transmuted-G family which extends the quadratic rank transmutation map pioneered by Shaw and Buckley (2007). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, genera...

The idea of symmetry, which is used to describe the shape of a probability distribution, is a key concept in the theory of probability. The use of symmetric and asymmetric distributions is common in statistical inference, decision-making, and probability calculations. This article introduces a novel asymmetric model for assessing risks under a skew...

Tis paper introduces and studies a unique probability distribution. Te maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the Anderson-Darling estimation methods all take into account a number of fnancial risk indicators, including the value-at-risk, tail-value-at-risk, tail variance, tail mean-variance, and...

Actuarial risks can be analyzed using heavy-tailed distributions, which provide adequate risk assessment. Key risk indicators, such as value-at-risk, tailed-value-at-risk (conditional tail expectation), tailed-variance, tailed-mean-variance, and mean excess loss function, are commonly used to evaluate risk exposure levels. In this study, we analyze...

Quality control testing under acceptance sampling plans involves inspecting a representative sample of products or materials from a larger lot or batch to determine whether the lot meets predetermined quality standards. In this research, the modified Lindley distribution is used as a model for lifetime study. When a life test is amputated at a pre-...

Continuous probability distributions can handle and express different data within the modeling process. Continuous probability distributions can be used in the disclosure and evaluation of risks through a set of well-known basic risk indicators. In this work, a new compound continuous probability extension of the reciprocal Rayleigh distribution is...

Citation: Yousof, H.M.; Goual, H.; Emam, W.; Tashkandy, Y.; Alizadeh, M.; Ali, M.M.; Ibrahim, M. An Alternative Model for Describing the Abstract: We provide a new extension of the exponential distribution with an emphasis on the practical elements of the model. Six different classical estimation methods were applied and compared. The main test was...

A novel flexible extension of the Chen distribution is defined and studied in this paper. Relevant statistical properties of the novel model are derived. For the actuarial risk analysis and evaluation, the maximum likelihood, weighted least squares, ordinary least squares, Cramer-von Mises, moments, and Anderson-Darling methods are utilized. For ac...

This paper introduces a new class of Balakrishnan distribution by extending the multimodal skew-normal distribution proposed by Chakraborty et al. (2015). Statistical properties of the new family of distributions are studied in detail. In particular, explicit expressions of the density and distribution function, moments, skewness, kurtosis and the...

Probability-based distributions might be able to explain risk exposure well. Usually, one number, or at the very least, a limited number of numbers called the key risk indicators (KRIs), are used to describe the level of risk exposure. These risk exposure values, which are undeniably the outcome of a specific model, are frequently referred to as es...

A modified version of Bagdonavičius-Nikulin goodness-of-fit statistical test is presented for validation under the right censor case. Simulation via Barzilai-Borwein algorithm is performed for assessing the right censorship estimation method. Four right censored data sets are analyzed under the new modified test statistic for checking the distribut...

We propose a new extension of the exponential distribution for right censored Bayesian and non-Bayesian distributional validation. The parameter of the new distribution is estimated using several conventional methods, including the Bayesian method. The likelihood estimates and the Bayesian estimates are compared using Pitman's closeness criteria. T...

After studying the mathematical properties of the Double Burr XII model, we present Bayesian and non-Bayesian estimation for its unknown parameters. Also, we constructed a new statistical test for goodness-of-fit in case of complete and censored samples. The modified test is developed based on the Nikulin-Rao-Robson statistic for validation. Simula...

When a life test is terminated at a predetermined time to decide whether to accept or refuse the submitted batches, the types of group sampling inspection plans (single, two, and multiple stages) are introduced. The tables in this study give the optimal number of groups for various confidence levels, examination limits, and values of the ratio of t...

The Poisson Topp Leone Burr XII distribution is studied mainly for illustrating its wide applicability under censored (engineering, economic and medical) real data sets. Four real data sets are analyzed, the Poisson Topp Leone Burr XII distribution is compared with nine Burr type XII extensions which provided the best fits. A modified Bagdonavičius...

A new extension of the inverse Weibull model is introduced and studied. Some of its statistical properties are derived. Different estimation methods are used for estimating the unknown parameter. We assessed the performance of all methods via simulation study. Two real data applications are used for comparing competitive estimation methods. The imp...

In this paper we present a new G family of probability distributions. Some of its mathematical properties are derived. Based on a special member of the new family, a single acceptance sampling plan is considered. The issue of a single sample plan when the lifetime test is truncated at a pre-determined period is discussed. For certain different acce...

Statistical distributions are important tools to model the characteristics of data sets such as right or left skewness, bi-modality or multi-modality observed in different applied sciences such as engineering, medicine, and finance, among others. The well-known distributions such as normal, Weibull, gamma, Lindley are extensively used because of th...

This paper introduces a new extension of the Gompertz function for estimating the survival rates. The actual survival rates from USA life tables 2015 is considered for assessment process under the ordinary least squares method. A real data application is presented under the maximum likelihood method. The new Gompertz function is compared with many...

A new modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test is presented and investigated for validity under the exponentiated Rayleigh generalized Chen distribution and the right censor case. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Four right ce...

We define and study a new compound G family of distributions. Some of its relevant mathematical properties are derived. Special case based on the Lomax model is studied and analyzed. Some new bivariate type G family of distributions using Clayton copula, Renyi's copula, Ali-Mikhail-Haq copula, Farlie-Gumbel-Morgenstern copula and its relevant modif...

This paper presents a novel two-parameter G family of distributions. Some relevant statistical properties such as the ordinary moments, incomplete moments and generating function are derived. Special attention is devoted to the standard Fréchet baseline model. Different classical estimation methods under uncensored schemes are considered such as th...

In this work, we introduced a new three-parameter Nadarajah-Haghighi model. We derived explicit expressions for some of it statistical properties. The Farlie Gumbel Morgenstern, modified Farlie Gumbel Morgenstern, Clayton, Renyi and Ali-Mikhail-Haq copulas are used for deriving some bivariate type extensions. We consider maximum likelihood, Cramér-...

In this article, we introduced the truncated versions (lower, upper and double) of xgamma distribution (Sen et al. 2016). In particular, different structural and distributional properties such as moments, popular entropy measures, order statistics and survival characteristics of the upper truncated xgamma distribution are discussed in detail. We br...

In this work, a new flexible extension of the Chen distribution is derived and studied. The new density accommodates the "unimodal right skewed", "unimodal left skewed", "bimodal right skewed" and "bimodal left skewed" shapes. The new hazard rate can be "decreasing-constant-increasing (bathtub)", "monotonically increasing", "upside down constant-in...

Inflated models are generally used whenever there is an excess number of frequencies at particular count. In this study, a three-inflated Poisson (ThIP) distribution is proposed by mixing the Poisson distribution and a distribution to a point mass at three. Some of its distribution properties and reliability characteristics are studied. A simulatio...

A new three-parameter lifetime model called the odd Burr Lomax (OBLo) is defined and studied. The density of the OBLo model can be asymmetric heavy tail right skewed density and symmetric density with different useful shapes. Hazard Rate Function (HRF) of the odd Burr Lomax can be "monotonically decreasing", "J-hazard rate function", "increasing-co...

A new compound Lomax model is proposed and analyzed. The novel distribution is derived based on compounding the zero truncated Poisson distribution and the exponentiated exponential Lomax distribution. The new density can be “monotonically left skewed”, “monotonically right skewed” and “symmetric” with various useful shapes. The new hazard rate can...

In this paper, a modified Chi-square goodness-of-fit test called the modified Bagdonavičius-Nikulin goodness-of-fit test statistic is investigated and the applied for distributional validation under the right censored case. The new modified goodness-of-fit test is presented and applied for the right censored data sets. The algorithm of the censored...

In this paper, a new flexible model with three-parameter alternative to exponential and Gompertz distributions is proposed. Some of its statistical properties are derived including quantities, moments, incomplete moments, moment of residual and reversed residual life. The parameters are estimated using the maximum likelihood method based on complet...

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right c...

In this paper, we introduce a new four-parameter distribution which is called Extended Exponentiated Chen (EE-C) distribution. Theoretical properties of this model including the hazard function, moments, conditional moments, mean residual life, mean past lifetime, coefficients of skewness and kurtosis, order statistics and asymptotic properties are...

A new lifetime distribution is proposed and its properties are studied. The new density function has a heavy right skew tails with different shapes. The new failure rate function can be "constant", "bathtub (U)", "increasing-constant", "decreasing-constant", "upside down" and "upside down-U". Complexity of the most integrals related to statistical...

In this paper, a new form of alpha-beta-skew distribution is proposed under Balakrishnan (2002) mechanism and investigated some of its related distributions. The most important feature of this new distribution is that it is versatile enough to support both unimodal and bimodal as well as multimodal behaviors of the distribution. The moments, distri...

Brief description of the book: Statistical distributions are important tools to model the characteristics of data sets such as right or left skewness, bi-modality or multi-modality observed in different applied sciences such as engineering, medicine, and finance, among others. The well-known distributions such as normal, Weibull, gamma, Lindley ar...

Recently there is a lot of research related to skewed distributions and their growing relevance in data analytics. In the present work we introduce a new generalized version of alpha beta skew normal distribution and some of its basic properties are investigated. Some extensions of the proposed distribution have also been studied. A simulation stud...

In this work, we propose and study a new discrete analogue of the Weibull class. Many useful properties such as ordinary moments; moment generating function; cumulant generating function; probability generating function; central moments and dispersion index are derived. Two special discrete versions are discussed theoretically, graphically, and num...

In this article, a new reciprocal Rayleigh extension called the Xgamma reciprocal Rayleigh model is defined and studied. relevant statistical properties are derived. Useful results related to the convexity and concavity are addressed. We discussed the estimation of the parameters using different estimation methods such as maximum likelihood estimat...

A generalization of Burr X model is proposed and studied. Some bivariate and multivariate type distributions are derived based on Clayton Copula, Farlie Gumbel Morgenstern Copula and Renyi's entropy. Various mathematical properties of this new distribution are derived and analyzed. Different estimation methods such as Cramér-von-Mises method, maxim...

We introduce and study a new version of the generalized Rayleigh distribution. Some of its properties are derived and numerically analyzed. Many bivariate and multivariate type distributions have been also derived based on Farlie Gumbel Morgenstern Copula, Clayton Copula and Renyi's entropy. We briefly describe different estimation methods namely,...

In this paper, we introduce a new lifetime distribution called the Topp-Leone Lindley distribution. Some of its structural properties including ordinary and incomplete moments, quantile function, moment generating function, characteristic function, cumulant generating function, moment of residual life and reversed residual life functions, stress-st...

We introduce a new continuous distribution based on the zero truncated Poisson model which accommodates many important failure rate shapes. Some of its mathematical properties are derived. The density of the new distribution can be expressed as a combination of exponentiated Weibull densities. The method of the maximum likelihood is considered to e...

After defining a new log-logistic model and studying its properties, some new bivariate type versions using “Farlie-Gumbel-Morgenstern Copula”, “modified Farlie-Gumbel-Morgenstern Copula”, “Clayton Copula” and “Renyi’s entropy Copula” are derived. Then, using the Bagdonavicius-Nikulin goodness-of-fit (BN-GOF) test for validation, we proposed a good...

In this paper, a new flexible version the exponentiated Weibull model is introduced and studied. The new model generalizes many new and well-known models. We are motivated to introduce and study the new model since its density exhibits various important shapes such as decreasing, unimodal, bimodal, inverse-N shaped, right skewed and left skewed. Th...

In this paper, a new form of log-alpha-skew distribution is proposed by the same methodology of Venegas et al. (2016) and investigated some of its related distributions. The moments and distributional properties of the proposed distribution are also discussed. Also, the appropriateness of this distribution are checked by performing the data fitting...

In this paper, we introduce a new extension of the Inverse Weibull distribution along with a number of its mathematical properties. Next, we construct a modified Chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic for censored and complete data. We describe the theory and the mechanism of the Yn 2 test statistic which can be...

In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The new density has a strong physical interpretation and can be a symmetric function and unimodal...

In this paper we have introduced a generalized version of alpha beta skew normal distribution in the same line of Sharafi et al. (2017) and investigated some of its basic properties. The extensions of the proposed distribution have also been studied. The appropriateness of the proposed distribution has been tested by comparing the values of Akaike...

In this paper, we first introduce a new extension of the exponentiated exponential distribution along with its several mathematical properties. Second, we construct a modified Chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic in presence of censored and complete data. We describe the theory and the mechanism of the Yn2 stat...

In previous chapters, the various sampling plans discussed were for small data obtained from the industry. In this modern era of big data, there are several situations where the data is obtained for the inspection or lot sentencing of the product from a huge data set. The study of big data has been becoming popular day by day, especially for the in...

Skip-lot sampling plans (SkSP) have been widely used in the industry where the lots come serially from the continuous production process and submitted for inspection. These sampling plans can be applied on attribute data and variable data. The operational procedure of SkSP scheme is different from the single sampling plan. A lot from the production...

Recently, group sampling plans based on truncated life tests have attracted the researchers, industries, practitioners and experimenters working in the areas of acceptance sampling and reliability analysis due to the several advantages over the ordinary acceptance sampling plans. In ordinary acceptance sampling plan schemes, single item is installe...

This book introduces a number of new sampling plans, such as time truncated life tests, skip sampling plans, resubmitted plans, mixed sampling plans, sampling plans based on the process capability index and plans for big data, which can be used for testing and inspecting products, from the raw-materials stage to the final product, in every industry...

Acceptance sampling is an important field of statistical quality control (SQC) to inspect the final product before it can be realized for consumers’ use. Acceptance sampling in its present form is due to the US Inspection Engineering Department. With the advent of the twenty-first century, many research papers in this field have been published in v...

In this chapter, several life distributions, which are used in statistical quality control, are considered along with few of the characteristics of these distributions. Most of these distributions are considered in the subsequent chapters.

Acceptance sampling approach is helpful in reducing the cost and time of the inspection of a submitted product. In this modern era, the reliability of the products is very high. The experimenters may wait a long time to record the required numbers of failures. Therefore, the time truncated life tests in sampling plans are used to reach a decision q...

During the manufacturing process of a product, the manufacturer is very careful from the initial raw material to the final stage of the product. He always tries to enhance the quality level of the product. But if even the product is manufactured using the same machines, in the same laboratory, using the same manpower and environment and at the same...

The Process Capability Index (PCI) has been widely used in the industry to manage the quality of product. It has become an important tool of Statistical Process Control (SPC) for the continuous improvement of the quality. The PCIs are used to make a relationship between process quality and specifications limits and take into consideration both magn...

In addition to sampling plans discussed in the previous chapters, there are some other sampling plans which are used in various situations. Incorporating the exponentially weighted moving average (EWMA) makes the traditional sampling plan more efficient in reducing the cost and time of inspection. Sampling plans using some loss function are also us...

In this work, we focus on some new theoretical and computational aspects of the Odd Lindley Lomax model. The maximum likelihood estimation method is used to estimate the model parameters. We show empirically the importance and flexibility of the new model in modeling two types of aircraft windshield lifetime data. This model is much better than exp...

A new distribution called the Weibull Generalized log logistic distribution is introduced along with a simple physical motivation. Several of its statistical properties are derived. Three applications are provided to illustrate the importance of the new distribution. The new distribution is shown to be better that other important competitive models...

In this paper, we introduce a new extension of Burr XII distribution called Topp Leone Generated Burr XII distribution. We derive some of its properties. Useful characterizations are presented. Simulation study is performed to assess the performance of the maximum likelihood estimators. Censored maximum likelihood estimation is presented in the gen...

We study a new family of distributions defined by the minimum of the Poisson random number of independent and identically distributed random variables having the Topp Leone-G distribution. Some mathematical properties of the new family are derived. Maximum likelihood estimation of the model parameters is investigated. Two special models of the new...

In this paper, we propose a new class of lifetime distributions called the Marshall-Olkin Generalized G Poisson family. The proposed family of distributions is constructed by compounding the Marshall-Olkin Generalized distribution with the truncated Poisson distribution. It can provide better fits than some of the known lifetime distributions and t...

We propose a new class of models called the Weibull Generalized-G family with two extra positive shape parameters, which extends several well-known models. We obtain some of its mathematical properties including ordinary and incomplete moments, generating function, order statistics, probability weighted moments, entropies, residual, and reversed re...

A family of continuous probability distributions which integrates recently introduced Marshall-Olkin-Kumaraswamy-G family and Beta Marshall-Olkin-G family of distributions is proposed. Probability density function , cumulative distribution function, moment generating function, moments and probability density function of order statistics of the prop...

In this article, we study an extension of the Fréchet model by using the odd Lindley-G family of distributions, which was introduced by Silva et. al (2017). Its some statistical properties such as quantile function, density shapes, moments, generating functions and order statistics are obtained. We estimate its parameters by maximum likelihood meth...