Papers by Professor Dr. Abdus Saboor
Frontier in Physics, 2024
and Ismail EAA (2024) A qualitative analysis of the artificial neural network model and numerical... more and Ismail EAA (2024) A qualitative analysis of the artificial neural network model and numerical solution for the nanofluid flow through an exponentially stretched surface.
Heliyon, 2024
This paper develops a novel two-parameter unit probability model which is the generalized form Ku... more This paper develops a novel two-parameter unit probability model which is the generalized form Kumaraswami distribution that exhibits greater flexibility compared to well-known existing distributions, attributed to its distinct hazard and density function shapes. Extensive analysis has been conducted to explore numerous statistical features of the specified distribution, specifically moments, and order statistics providing explicit expressions for these measures. The maximum likelihood estimation is employed to estimate the model parameters and a numerical simulation analysis confirms the consistency of this estimation approach. Furthermore, the applicability of the specified model is demonstrated by considering four real data sets, showcasing its effectiveness in capturing the characteristics of real life data. The proposed model shows promise as a versatile tool for analyzing diverse data sets in a wide range of fields.
DOAJ (DOAJ: Directory of Open Access Journals), Feb 1, 2018
Research Article, Apr 17, 2024
The premise of extreme value theory focuses on the stochastic behaviour and occurrence of extreme... more The premise of extreme value theory focuses on the stochastic behaviour and occurrence of extreme observations in an event that is random. Traditionally for univariate case, the behaviour of the maxima is described either by the types-I, types-II or types-III extreme value distributions, primarily known as the Gumbel, Fréchet or reversed Weibull models. These are all particular cases of the generalized extreme value (GEV) model. However, in real-world scenario, these incidents take place as a consequence of concurrent dependent random events, where the relationship
between the two variables is unidirectional or asymmetrical. [1] introduced a rigorous univariate extension of GEV distribution involving an additional parameter, the 𝑞− generalized extreme value (𝑞 − GEV) distribution, as well as the 𝑞− Gumbel distribution. The prime interest of this paper lies in conceptualizing a novel approach to model bivariate (EV) data, arising naturally from independent 𝑞 −GEV random variables. This is achieved via the transformation of variables technique by establishing the resulting supports. Concisely, a technique is developed to model
interdependent bivariate observations consisting of extreme values in terms of 𝑞−GEV probability density functions. Besides, we employed the suggested technique to a bivariate flood data set and demonstrate the competitiveness of the proposed bivariate 𝑞 − GEV. Additionally, conventional method to propose the newly defined bivariate (𝑞 − GEV) distribution with bivariate 𝑞− Gumbel distribution (a special case for 𝜉 → 0) has also been established with related inferences and application to climate data.
Mathematica Slovaca, 2022
In this article, we develop a new general family of distributions aimed at unifying some well-est... more In this article, we develop a new general family of distributions aimed at unifying some well-established lifetime distributions and offering new work perspectives. A special family member based on the so-called modified Weibull distribution is highlighted and studied. It differs from the competition with a very flexible hazard rate function exhibiting increasing, decreasing, constant, upside-down bathtub and bathtub shapes. This panel of shapes remains rare and particularly desirable for modeling purposes. We provide the main mathematical properties of the special distribution, such as a tractable infinite series expansion of the probability density function, moments of several kinds (raw, incomplete, probability weighted…) with discussions on the skewness and kurtosis. The stochastic ordering structure and stress-strength parameter are also considered, as well as the basics of the order statistics. Then, an emphasis is put on the inferential features of the related model. In parti...
Integral Transforms and Special Functions
Conway [A Lagrangian method for deriving new indefinite integrals of special functions. Integral ... more Conway [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015;26:812– 824] introduced a new and simple method named the ‘Lagrangian method’ for deriving indefinite integrals of both elementary and special functions, provided the function satisfies the second-order linear differential equation. In this paper, different Meijer’s G-functions have been used for deriving indefinite integrals, which satisfy second-order differential equations. We have derived recurrence relations and the integration of those recurrence relations by the Lagrangian method.Wehave discussed the integration of Euler identity, which is given in terms of Meijer’s G-function. Different additional relations of Meijer’s G-functions have also been discussed.
Journal of Computational and Applied Mathematics, 2018
The last decade is full on new classes of distributions that become precious for applied statisti... more The last decade is full on new classes of distributions that become precious for applied statisticians. Extending known distributions by adding parameters enables us to obtain more flexible models. We provide some new mathematical properties of the transmuted generalized gamma distribution defined from the family pioneered by Aryal and Tsokos (2011). We derive explicit expressions for some of its mathematical quantities. We present maximum likelihood and Bayesian estimators for the model parameters. The different estimators are compared using extensive numerical simulations. For the sake of illustration, we apply our proposed methodology to two real data sets, thus proving empirically that the current distribution is a simple alternative for lifetime data.
Filomat, 2017
Canada EM provost@stats.uwo.ca AU Ortega Edwinm M. AF Universidade de S?o Paulo, Departamento de ... more Canada EM provost@stats.uwo.ca AU Ortega Edwinm M. AF Universidade de S?o Paulo, Departamento de Ci?ncias Exatas, Piracicaba, Brazil EM edwin@usp.br KW Generalized modifiedWeibull distribution % Goodness-of-fit statistic % Lifetime data % Transmuted family % Weibull distribution KR nema A profusion of new classes of distributions has recently proven useful to applied statisticians working in various areas of scientific investigation. Generalizing existing distributions by adding shape parameters leads to more flexible models. We define a new lifetime model called the transmuted generalized modified Weibull distribution from the family proposed by Aryal and Tsokos [1], which has a bathtub shaped hazard rate function. Some structural properties of the new model are investigated. The parameters of this distribution are estimated using the maximum likelihood approach. The proposed model turns out to be quite flexible for analyzing positive data. In fact, it can provide better fits than ...
Applied Mathematical Modelling, 2016
Abstract We introduce a new distribution, so-called beta Sarhan–Zaindin modified Weibull (BSZMW) ... more Abstract We introduce a new distribution, so-called beta Sarhan–Zaindin modified Weibull (BSZMW) distribution, which extends a number of recent distributions, among which the modified-Weibull, the exponentiated modified-Weibull, beta Weibull and beta linear failure rate distributions. Various structural properties of the distribution are obtained (sometimes in terms of Meijer’s G -function), such as the moments, moment generating function, conditional moments, mean deviations, entropy, order statistics, mean and variance of the (reversed) residual life and maximum likelihood estimators as well as the observed information matrix. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The BSZMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in meteorology. It is shown that, the distribution has a superior performance among the compared distributions as evidenced by some goodness-of-fit tests. As well, some statistical functions associated with these data such as the return level and mean deviation about the return level are obtained.
Mathematica Slovaca, 2020
In this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely ... more In this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed biva...
Integral Transforms and Special Functions, Mar 16, 2023
Conway [A Lagrangian method for deriving new indefinite integrals
of special functions. Integral... more Conway [A Lagrangian method for deriving new indefinite integrals
of special functions. Integral Transforms Spec Funct. 2015;26:812–
824] introduced a new and simple method named the ‘Lagrangian
method’ for deriving indefinite integrals of both elementary and special
functions, provided the function satisfies the second-order linear
differential equation. In this paper, different Meijer’s G-functions
have been used for deriving indefinite integrals, which satisfy
second-order differential equations. We have derived recurrence
relations and the integration of those recurrence relations by the
Lagrangian method.Wehave discussed the integration of Euler identity,
which is given in terms of Meijer’s G-function. Different additional
relations of Meijer’s G-functions have also been discussed.
In this paper, we propose a new distribution obtained by mixing gamma and geometric distributions... more In this paper, we propose a new distribution obtained by mixing gamma and geometric distributions. We discuss different shapes of the probability density function and the hazard rate functions. We study several statistical properties. The maximum likelihood estimation method is performed for estimating the parameters. We determine the observed information matrix and discuss inference. Illustrative three hydrology data sets are given to show the flexibility and potentiality of the proposed distribution.
Annals of Data Science, 2019
In this paper, we introduce a flexible modified beta linear exponential (MBLE) distribution. Our ... more In this paper, we introduce a flexible modified beta linear exponential (MBLE) distribution. Our motivation, besides others are there, dues to its ability in hydrology applications. We investigate a set of its statistical properties for supporting such applications, like moments, moment generating function, conditional moments, mean deviations, entropy, mean and variance (reversed) residual life and maximum likelihood estimators with observed information matrix. The distribution can accommodate both decreasing and increasing hazard rates as well as upside down bathtub and bathtub shaped hazard rates. Moreover, several distributions arise as special cases of the distribution. The MBLE distribution with others are fitted to two hydrology data sets. It is shown that, the MBLE distribution is the best fit among the compared distributions based on nine goodness-of-fit statistics among them the Corrected Akaike information criterion, Hannan-Quinn information criterion, Anderson-Darling and Kolmogorov-Smirnov p value. Consequently, some parameters of these data are obtained such as return level, conditional mean, mean deviation about the return level, risk of failure for designing hydraulic structures. Finally, we hope that this model will be able to attract wider applicability in hydrology and other life areas.
Computational Statistics, 2018
We introduce a flexible modified beta modified-Weibull model, which can accommodate both monotoni... more We introduce a flexible modified beta modified-Weibull model, which can accommodate both monotonic and non-monotonic hazard rates such as a useful long bathtub shaped hazard rate in the middle. Several distributions can be obtained as special cases of the new model. We demonstrate that the new density function is a linear combination of modified-Weibull densities. We obtain the ordinary and central moments, generating function, conditional moments and mean deviations, residual life functions, reliability measures and mean and variance (reversed) residual life. The method of maximum likelihood and a Bayesian procedure are used for estimating the model parameters. We compare the fits of the new distribution and other competitive
Mediterranean Journal of Mathematics, 2017
We introduce and study a new distribution called the odd loglogistic modified Weibull (OLLMW) dis... more We introduce and study a new distribution called the odd loglogistic modified Weibull (OLLMW) distribution. Various of its structural properties are obtained in terms of Meijer's G-function, such as the moments, generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes varying skewness and takes all possible forms of hazard rate function. We fit the OLLMW and some competitive models to two data sets and prove empirically that the new model has a superior performance among the compared distributions as evidenced by some goodness-of-fit statistics.
Hacettepe Journal of Mathematics and Statistics, 2015
Significant progress has been made towards the generalization of some well-known lifetime models,... more Significant progress has been made towards the generalization of some well-known lifetime models, which have been successfully applied to problems arising in several areas of research. In this paper, some properties of the new Kumaraswamy exponential-Weibull (KwEW) distribution are provided. This distribution generalizes a number of well-known special lifetime models such as the Weibull, exponential, Rayleigh, modified Rayleigh, modified exponential and exponentiated Weibull distributions, among others. The beauty and importance of the new distribution lies in its ability to model monotone and nonmonotone failure rate functions, which are quite common in environmental studies. We derive some basic properties of the KwEW distribution including ordinary and incomplete moments, skewness, kurtosis, quantile and generating functions, mean deviations and Shannon entropy. The method of maximum likelihood and a Bayesian procedure are used for estimating the model parameters. By means of a real lifetime data set, we prove that the new distribution provides a better fit than the Kumaraswamy Weibull, Marshall-Olkin exponential-Weibull, extended Weibull, exponential-Weibull and Weibull models. The application indicates that the proposed model can give better fits than other well-known lifetime distributions.
2010 6th International Conference on Emerging Technologies (ICET), 2010
... a verb in TL [5, 6]. Three cases were found in which the subjective complement of ... 6 types... more ... a verb in TL [5, 6]. Three cases were found in which the subjective complement of ... 6 types oflexical-semantic divergence for Urdu-to-English translation are identified and ... 1] D. Gupta and N. Chatterjee, Study of divergence for example based English-Hindi machine translation ...
Journal of Mathematics, 2021
In this paper, a new confluent hypergeometric gamma function and an associated confluent hypergeo... more In this paper, a new confluent hypergeometric gamma function and an associated confluent hypergeometric Pochhammer symbol are introduced. We discuss some properties, for instance, their different integral representations, derivative formulas, and generating function relations. Different special cases are also considered.
Mathematica Slovaca, 2020
In this paper, we propose a new three-parameter modified Burr XII distribution based on the stand... more In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.
Mathematica Slovaca, 2019
We introduce and study the beta exponentiated Nadarajah-Haghighi model, which has increasing, dec... more We introduce and study the beta exponentiated Nadarajah-Haghighi model, which has increasing, decreasing, upside-down bathtub and bathtub shaped hazard functions. Some of its mathematical properties are determined including a power series for the quantile function. We perform a Monte Carlo simulation study to assess the finite sample behavior of the maximum likelihood estimates of the parameters. We define a new regression model based on the new distribution. The potentiality of this regression model is proved empirically by means of a real dataset related to diabetic retinopathy study.
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Papers by Professor Dr. Abdus Saboor
between the two variables is unidirectional or asymmetrical. [1] introduced a rigorous univariate extension of GEV distribution involving an additional parameter, the 𝑞− generalized extreme value (𝑞 − GEV) distribution, as well as the 𝑞− Gumbel distribution. The prime interest of this paper lies in conceptualizing a novel approach to model bivariate (EV) data, arising naturally from independent 𝑞 −GEV random variables. This is achieved via the transformation of variables technique by establishing the resulting supports. Concisely, a technique is developed to model
interdependent bivariate observations consisting of extreme values in terms of 𝑞−GEV probability density functions. Besides, we employed the suggested technique to a bivariate flood data set and demonstrate the competitiveness of the proposed bivariate 𝑞 − GEV. Additionally, conventional method to propose the newly defined bivariate (𝑞 − GEV) distribution with bivariate 𝑞− Gumbel distribution (a special case for 𝜉 → 0) has also been established with related inferences and application to climate data.
of special functions. Integral Transforms Spec Funct. 2015;26:812–
824] introduced a new and simple method named the ‘Lagrangian
method’ for deriving indefinite integrals of both elementary and special
functions, provided the function satisfies the second-order linear
differential equation. In this paper, different Meijer’s G-functions
have been used for deriving indefinite integrals, which satisfy
second-order differential equations. We have derived recurrence
relations and the integration of those recurrence relations by the
Lagrangian method.Wehave discussed the integration of Euler identity,
which is given in terms of Meijer’s G-function. Different additional
relations of Meijer’s G-functions have also been discussed.
between the two variables is unidirectional or asymmetrical. [1] introduced a rigorous univariate extension of GEV distribution involving an additional parameter, the 𝑞− generalized extreme value (𝑞 − GEV) distribution, as well as the 𝑞− Gumbel distribution. The prime interest of this paper lies in conceptualizing a novel approach to model bivariate (EV) data, arising naturally from independent 𝑞 −GEV random variables. This is achieved via the transformation of variables technique by establishing the resulting supports. Concisely, a technique is developed to model
interdependent bivariate observations consisting of extreme values in terms of 𝑞−GEV probability density functions. Besides, we employed the suggested technique to a bivariate flood data set and demonstrate the competitiveness of the proposed bivariate 𝑞 − GEV. Additionally, conventional method to propose the newly defined bivariate (𝑞 − GEV) distribution with bivariate 𝑞− Gumbel distribution (a special case for 𝜉 → 0) has also been established with related inferences and application to climate data.
of special functions. Integral Transforms Spec Funct. 2015;26:812–
824] introduced a new and simple method named the ‘Lagrangian
method’ for deriving indefinite integrals of both elementary and special
functions, provided the function satisfies the second-order linear
differential equation. In this paper, different Meijer’s G-functions
have been used for deriving indefinite integrals, which satisfy
second-order differential equations. We have derived recurrence
relations and the integration of those recurrence relations by the
Lagrangian method.Wehave discussed the integration of Euler identity,
which is given in terms of Meijer’s G-function. Different additional
relations of Meijer’s G-functions have also been discussed.
is a particular case of this distribution, the latter is referred to as a gammaWeibull distribution. Numerous distributions
such as the Rayleigh, half-normal and Maxwell distributions
can also be obtained as special cases. The moment generating function of a gamma-Weibull random variable is derived by making use of the inverse Mellin transform technique and expressed in terms of generalized hypergeometric functions. This provides computable
representations of the moment generating functions of several of the distributions that were identified as particular cases. Other statistical functions such as the cumulative distribution function of a gamma-Weibull random variable, its moments, hazard rate and associated entropy are also given in closed form. The proposed extension is utilized to model two data sets. The gamma--Weibull distribution provides a better fit than the two-parameter Weibull
model or its shifted counterpart, as measured by the Anderson-Darling and Cramer-von Mises statistics.
Al-Saqabi et al. (2003) defined a univariate gamma-type function involving the confluent hypergeometirc function of two variables (Erdélyi, 1953) and discussed some associated statistical functions. We define a bivariate generalized gamma-type function using the confluent hypergeometric
function of two variables and discuss some of its statistical functions, including the moment generating function, in terms of the G-function. This provides computable representations of the moment generating functions of
several of the distributions that were identified as particular cases. Many other distributions such as the Rayleigh, half-normal and Maxwell distributions can also be obtained as special cases of the bivariate gamma-type density function.
The cumulative distribution function is also provided in closed form.