Muhammad Nauman Khan | Kohat University of science and technology (original) (raw)

Papers by Muhammad Nauman Khan

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.

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.

A profusion of new classes of distributions has recently showed its usefulness to applied statist... more A profusion of new classes of distributions has recently showed its usefulness to applied statisticians working in various areas of studies. Generalizing existing
distributions by adding extra parameters to an existing family of distribution functions leads to more flexible models. In this article, we define a new
three-parameter lifetime model called the weighted modified Weibull distribution. Various statistical properties of the distribution are derived.
The estimation of parameters is discussed by using the method of maximum likelihood. Finally, the superiority of the proposed distribution is shown by analyzing four well-known lifetime datasets.

Development and application of probability models in data analysis are of major importance for al... more Development and application of probability models in data analysis are of major importance for all sciences. Therefore, we introduce a new model called a power log-Dagum distribution defined on the entire real line. The model contains many new sub-models: power logistic, linear log-Dagum, linear logistic and log-Dagum distributions among them. Some properties of the model including three different estimation procedures are justified. The model exhibits various shapes for the density and hazard rate functions. Moreover, the estimation procedures are compared using simulation studies. Finally, the model with others are fitted to three data sets and it shows a better fit than the compared distributions defined on the real line.

In this paper, we introduce a new family of distributions extending the odd family of distributio... more In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then we study a special case dealing with the standard loglogistic distribution and the modified Weibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions by fitting a sub-model of this family to two practical data sets.

University POLITEHNICA of Bucharest series A Applied Mathematics and Physics, 2018

A two-parameter weighted Nadarajah and Haghighi (WNH) distribution is proposed and studied in thi... more A two-parameter weighted Nadarajah and Haghighi (WNH) distribution is proposed and studied in this article. The proposed distribution can be viewed as an alternate model to some of the classical two-parameter distributions such as the Weibull, gamma, exponentiated half-logistic and exponenti-ated exponential distributions. We discuss some of its mathematical functions. Maximum likelihood estimation method is utilized to estimate the unknown parameters of the proposed distribution. A Monte Carlo simulation study is performed to assess the performance of maximum likelihood estimates. We compare the fits of the new distribution and other competitive models to four real data sets. We prove empirically that the new distribution gives the best fit among these distributions based on the Anderson–Darling and Cramér–von Mises goodness–of–fit statistics.

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 models to two real data sets. We prove empirically that the new distribution gives the best fit among these distributions based on several goodness-of-fit statistics.

Hacettepe Journal of Mathematics and Statistics, 2015

ABSTRACT Significant progress has been made towards the generalization of some well--known lifeti... more ABSTRACT 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 non-monotone 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.

We introduce and study a new distribution called the odd log– logistic modified Weibull (OLLMW) d... more We introduce and study a new distribution called the odd log– logistic 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. Mathematics Subject Classification (2010). 60E05, 62E15, 62F10.

A profusion of new classes of distributions has recently proven useful to applied statisticians w... more 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 related distributions as measured by the Anderson-Darling (A *) and Cramér-von Mises (W *) statistics, which is illustrated by applying it to two real data sets. It may serve as a viable alternative to other distributions for modeling positive data arising in several fields of science such as hydrology, biostatistics, meteorology and engineering.

We introduce a new distribution, so-called Beta Sarhan-Zaindin modified Weibull (BSZMW) distribut... more 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 {\color{red}along} with other distributions are fitted to two sets of data, {\color{red}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.

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 non-monotone 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.

Hacettepe Journal of Mathematics and Statistics, 2014

A new five-parameter model called the modified beta Weibull probability distribution is being int... more A new five-parameter model called the modified beta Weibull probability distribution is being introduced in this paper. This model turns out to be quite flexible for analyzing positive data and has bathtub and upside down bathtub hazard rate function. Our main objectives are to obtain representations of certain statistical functions and to estimate the parameters of the proposed distribution. As an application, the probability density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.

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.

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.

A profusion of new classes of distributions has recently showed its usefulness to applied statist... more A profusion of new classes of distributions has recently showed its usefulness to applied statisticians working in various areas of studies. Generalizing existing
distributions by adding extra parameters to an existing family of distribution functions leads to more flexible models. In this article, we define a new
three-parameter lifetime model called the weighted modified Weibull distribution. Various statistical properties of the distribution are derived.
The estimation of parameters is discussed by using the method of maximum likelihood. Finally, the superiority of the proposed distribution is shown by analyzing four well-known lifetime datasets.

Development and application of probability models in data analysis are of major importance for al... more Development and application of probability models in data analysis are of major importance for all sciences. Therefore, we introduce a new model called a power log-Dagum distribution defined on the entire real line. The model contains many new sub-models: power logistic, linear log-Dagum, linear logistic and log-Dagum distributions among them. Some properties of the model including three different estimation procedures are justified. The model exhibits various shapes for the density and hazard rate functions. Moreover, the estimation procedures are compared using simulation studies. Finally, the model with others are fitted to three data sets and it shows a better fit than the compared distributions defined on the real line.

In this paper, we introduce a new family of distributions extending the odd family of distributio... more In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then we study a special case dealing with the standard loglogistic distribution and the modified Weibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions by fitting a sub-model of this family to two practical data sets.

University POLITEHNICA of Bucharest series A Applied Mathematics and Physics, 2018

A two-parameter weighted Nadarajah and Haghighi (WNH) distribution is proposed and studied in thi... more A two-parameter weighted Nadarajah and Haghighi (WNH) distribution is proposed and studied in this article. The proposed distribution can be viewed as an alternate model to some of the classical two-parameter distributions such as the Weibull, gamma, exponentiated half-logistic and exponenti-ated exponential distributions. We discuss some of its mathematical functions. Maximum likelihood estimation method is utilized to estimate the unknown parameters of the proposed distribution. A Monte Carlo simulation study is performed to assess the performance of maximum likelihood estimates. We compare the fits of the new distribution and other competitive models to four real data sets. We prove empirically that the new distribution gives the best fit among these distributions based on the Anderson–Darling and Cramér–von Mises goodness–of–fit statistics.

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 models to two real data sets. We prove empirically that the new distribution gives the best fit among these distributions based on several goodness-of-fit statistics.

Hacettepe Journal of Mathematics and Statistics, 2015

ABSTRACT Significant progress has been made towards the generalization of some well--known lifeti... more ABSTRACT 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 non-monotone 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.

We introduce and study a new distribution called the odd log– logistic modified Weibull (OLLMW) d... more We introduce and study a new distribution called the odd log– logistic 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. Mathematics Subject Classification (2010). 60E05, 62E15, 62F10.

A profusion of new classes of distributions has recently proven useful to applied statisticians w... more 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 related distributions as measured by the Anderson-Darling (A *) and Cramér-von Mises (W *) statistics, which is illustrated by applying it to two real data sets. It may serve as a viable alternative to other distributions for modeling positive data arising in several fields of science such as hydrology, biostatistics, meteorology and engineering.

We introduce a new distribution, so-called Beta Sarhan-Zaindin modified Weibull (BSZMW) distribut... more 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 {\color{red}along} with other distributions are fitted to two sets of data, {\color{red}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.

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 non-monotone 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.

Hacettepe Journal of Mathematics and Statistics, 2014

A new five-parameter model called the modified beta Weibull probability distribution is being int... more A new five-parameter model called the modified beta Weibull probability distribution is being introduced in this paper. This model turns out to be quite flexible for analyzing positive data and has bathtub and upside down bathtub hazard rate function. Our main objectives are to obtain representations of certain statistical functions and to estimate the parameters of the proposed distribution. As an application, the probability density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.