Department Of Mathematics And Statistics

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Browsing Department Of Mathematics And Statistics by Author "Arshad, Mohd"

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    Modeling Bivariate Data Using Linear Exponential and Weibull Distributions as Marginals
    (De Gruyter Open Ltd, 2023-08-04T00:00:00) Arshad, Mohd; Pathak, Ashok Kumar; Azhad, Qazi J.; Khetan, Mukti
    Modeling bivariate data with different marginals is an important problem and have numerous applications in diverse disciplines. This paper introduces a new family of bivariate generalized linear exponential Weibull distribution having generalized linear and exponentiated Weibull distributions as marginals. Some important quantities like conditional distributions, conditional moments, product moments and bivariate quantile functions are derived. Concepts of reliability and measures of dependence are also discussed. The methods of maximum likelihood and Bayesian estimation are considered to estimate model parameters. Monte Carlo simulation experiments are performed to demonstrate the performance of the estimators. Finally, a real data application is also discussed to demonstrate the usefulness of the proposed distribution in real-life situations. � 2023 Mathematical Institute Slovak Academy of Sciences.
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    A New Alpha Power Transformed Weibull Distribution: Properties and Applications
    (CRC Press, 2023-03-16T00:00:00) Pathak, Ashok Kumar; Arshad, Mohd; Bakshi, Sanjeev; Khetan, Mukti; Mangla, Sherry
    The Weibull distribution is one of the most widely used distributions in applied sciences and has been extensively utilized in reliability and survival analysis. By introducing additional parameters, several generations of the Weibull distribution have been proposed in the recent past to enhance the flexibility of the model. In this chapter, we introduced a three-parameter new alpha power transformed Weibull distribution. New alpha power transformed exponential, Weibull, Rayleigh, and exponential distributions are important sub-models of the proposed distribution. We study several statistical properties of the proposed distribution. Estimation of parameters using the method of maximum likelihood, weighted least squares, and Anderson Darling are discussed. Finally, some real data sets are also considered to demonstrate the applicability of the proposed distribution. � 2023 Mir Masoom Ali, Irfan Ali, Haitham M. Yousof and Mohamed Ibrahim.
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    A Novel Bivariate Generalized Weibull Distribution with Properties and Applications
    (Taylor and Francis Ltd., 2023-09-09T00:00:00) Pathak, Ashok Kumar; Arshad, Mohd; J. Azhad, Qazi; Khetan, Mukti; Pandey, Arvind
    Univariate Weibull distribution is a well known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with aging properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations. � 2023 Taylor & Francis Group, LLC.
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    Record-based transmuted generalized linear exponential distribution with increasing, decreasing and bathtub shaped failure rates
    (Taylor and Francis Ltd., 2022-07-29T00:00:00) Arshad, Mohd; Khetan, Mukti; Kumar, Vijay; Pathak, Ashok Kumar
    The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He. The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, R�nyi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cram�r-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data sets illustrate the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded. � 2022 Taylor & Francis Group, LLC.
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    Short-term forecasting of the COVID-19 outbreak in India
    (Oxford University Press, 2021-05-28T00:00:00) Mangla, Sherry; Pathak, Ashok Kumar; Arshad, Mohd; Haque, Ubydul
    As the outbreak of coronavirus disease 2019 (COVID-19) is rapidly spreading in different parts of India, a reliable forecast for the cumulative confirmed cases and the number of deaths can be helpful for policymakers in making the decisions for utilizing available resources in the country. Recently, various mathematical models have been used to predict the outbreak of COVID-19 worldwide and also in India. In this article we use exponential, logistic, Gompertz growth and autoregressive integrated moving average (ARIMA) models to predict the spread of COVID-19 in India after the announcement of various unlock phases. The mean absolute percentage error and root mean square error comparative measures were used to check the goodness-of-fit of the growth models and Akaike information criterion for ARIMA model selection. Using COVID-19 pandemic data up to 20 December 2020 from India and its five most affected states (Maharashtra, Karnataka, Andhra Pradesh, Tamil Nadu and Kerala), we report 15-days-ahead forecasts for cumulative confirmed cases and the number of deaths. Based on available data, we found that the ARIMA model is the best-fitting model for COVID-19 cases in India and its most affected states. � 2021 The Author(s) 2021.