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Lishamol Tomy

Mahatma Gandhi University, Kottayam, Statistics, Faculty Member

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Working as Associate Professor and Doctoral Research Supervisor. Research interests in Data Analysis, Distribution Theory, Time Series and Statistics. The recipient of prestigious Jan Tinbergen Award of International Statistical Institute, Netherlands. Completed PG with first rank and did doctoral studies with UGC-JRF.

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Ademolu Adenuga

UNIOSUN (Osun State University)

alireza shirvani

mohammad khayyer

Alireza Ghasemizad

catherine vaziri

hassanreza zeinabadi

hamid shafizadeh

Hamed Taheri Kia

Institute of Social and Cultural Studies

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Papers by Lishamol Tomy

A Statistical Study on Political Awareness among Youngsters in India

Iranian Journal of Educational Sociology

Nowadays, young people are spending the majority of their time on social media, using various pla... more Nowadays, young people are spending the majority of their time on social media, using various platforms like WhatsApp, Facebook, Instagram, etc. It is a common perception that these media have become the new sources of information, which progressively converts into knowledge. It is interesting to check whether they use those sources to achieve knowledge or not. The main focal point of this study is to understand the political engagement, knowledge, and outlook of college-studying youngsters in India. It studies the factors influencing political awareness and examines the influence of politics and politicians on the involvement of youngsters in politics. The findings show that social media has a significant influence on political issues, but they are also more corrupted.

The Inverted Modified Lindley Distribution

Journal of statistical theory and practice, Jun 18, 2020

This paper introduces a new inverted distribution derived from the modified Lindley distribution,... more This paper introduces a new inverted distribution derived from the modified Lindley distribution, and called the inverted modified Lindley. Its properties are derived and parameter is estimated by the methods of moments and maximum likelihood. The nice performance of the obtained estimates is validated by means of a simulation study. The adaptability of the new single parameter model is communicated by using three examples of real data and is depicted graphically.

The Truncated Modified Lindley Generated Family of Distributions

CRC Press eBooks, Mar 16, 2023

A comparative study of various estimation methods for modified Lindley distribution

Biometrics & Biostatistics International Journal, Jul 5, 2022

In this section, we concentrate on the estimation of parameter β , with an assumption that β is u... more In this section, we concentrate on the estimation of parameter β , with an assumption that β is unknown. Here, we consider estimating the parameter of the ML distribution using the methods, which include Maximum Likelihood (ML), Method of Moment (MOM) estimation, least squares (LS) and Weighted Least squares (WLS) estimation, and Cram´er-von Mises (CVM) estimation. ML estimation Consider (y 1 , y 2 , ..., y n) to be a random sample from the ML distribution with parameter β , with pdf defined in Equation (1). The log-likelihood (LL) function is given by The ML estimate of β , β  is defined as

Statistical study on challenges faced by students during lockdown due to COVID-19

Biometrics & Biostatistics International Journal, Dec 24, 2021

Due to the COVID-19 pandemic, the worldwide education system has been rigorously affected, follow... more Due to the COVID-19 pandemic, the worldwide education system has been rigorously affected, following the shutdown of schools and colleges/universities since March 2020 in order to prevent the spread of the virus. Conventional classrooms shifted to online classrooms which profoundly impacted teachers’ and students’ closed interaction, making a paradigm shift in the teaching-learning process. The Covid-19 Pandemic transformed the whole education process to online which has been transited to e-learning in most universities worldwide. The transition to a new environment of education, learners need special social care to improve their concentration and motivation to online learning in such a crucial crisis. The purpose of this study was to look out for the challenges and obstacles encountered in learning during the lockdown and if they were raising the mental stress in students. The study is based on a primary data collected from Kerala, India.

A new modified Lindley distribution with properties and applications

Journal of Statistics and Management Systems, Apr 18, 2021

Abstract This paper introduces a new one-parameter distribution derived from the Lindley distribu... more Abstract This paper introduces a new one-parameter distribution derived from the Lindley distribution, called the modified Lindley distribution. Its main feature is to operate a simple trade-off between the exponential and Lindley distributions, offering an interesting alternative to these two well-established distributions. We study the main properties of the proposed distribution, with a special emphasis on its moments, reliability parameter and asymptotic distributions of the extreme order statistics. Then, inferential considerations are explored. We discuss the parameter estimation by the moments and maximum likelihood methods. Three applications reveal that the new model has the ability to fit well practical data sets.

A retrospective study on Lindley distribution

Biometrics & Biostatistics International Journal, Apr 3, 2018

Generalizations make a distribution more flexible especially for studying the tail properties. Th... more Generalizations make a distribution more flexible especially for studying the tail properties. There exist many generalized family of continuous univariate distributions. In this article, a survey on Lindley distribution, its extensions and classes is conducted. Several available generalizations of the distribution are reviewed and recent trends in the construction of generalized classes are discussed.

Reliability Test Plan for an Extended Birnbaum-Saunders Distribution

Journal of reliability and statistical studies, Jun 22, 2021

Birnbaum-Saunders distribution has been widely studied in statistical literature because this dis... more Birnbaum-Saunders distribution has been widely studied in statistical literature because this distribution accommodates several interesting properties. The purpose of this paper is to introduce a new parametric distribution based on the Birnbaum-Saunders model and develop a new acceptance sampling plans for derived extended Birnbaum-Saunders distribution when the mean lifetime test is truncated at a predetermined time. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure a specified mean lifetime worked out. The results are illustrated by a numerical example. The operating characteristic functions of the sampling plans and producer's risk and the ratio of true mean life to a specified mean life that ensures acceptance with a pre-assigned probability are tabulated. This paper presents relevant characteristics of the new distribution and a new acceptance sampling plans when the lifetime of a product adopts an extended Birnbaum-Saunders distribution. Based on this study, the optimal number of testers demanded is decreases as test termination time increases. Moreover, the operating characteristic values increases as the mean life ratio increases,

On a new distribution based on the arccosine function

Arabian Journal of Mathematics, Aug 9, 2021

This note focuses on a new one-parameter unit probability distribution centered around the invers... more This note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be "round mesokurtic" and "left skewed". With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

The Marshall-Olkin Extended Power Lomax Distribution with Applications

Pakistan Journal of Statistics and Operation Research, Jun 3, 2020

In this article, we define a new four-parameter model called Marshall-Olkin extended power Lomax ... more In this article, we define a new four-parameter model called Marshall-Olkin extended power Lomax distribution and study its properties. Limiting distributions of sample maxima and sample minima are derived. The reliability of a system when both stress and strength follows the new distribution is discussed and associated characteristics are computed for a simulated data. Finally, utilizing maximum likelihood estimation, the goodness of the distribution is tested for a real data.

The Weibull Distribution: A Revisit

Abstract Weibull distribution is the most popular model in modeling data from various fields. Fro... more Abstract Weibull distribution is the most popular model in modeling data from various fields. From its introduction, comprehensive work has been done on this model providing distinct interpretations, constructions, generalizations, inferential methods, discrete cases and extensions to bivariate and multivariate. More than 4000 papers have appeared describing all these aspects and developments. This paper provides a review on the historical background and parallel developments of the Weibull distribution. Further, various generalizations and applications of the Weibull distribution are described. Keywords: Bivariate distribution, exponential distribution, hazard rate function, probability density function, Weibull Distribution Cite this Article Jiju Gillariose, Lishamol Tomy. The Weibull Distribution: A Revisit. Research & Reviews: Journal of Statistics. 2020 ; 9(1):16–26p.

A new discrete distribution on integers: Analytical and applied study on stock exchange and flood data

Journal of Statistics and Management Systems, Jul 29, 2022

The Poisson-Lindley difference model with application to discrete stock price change

International Journal of Modelling and Simulation, Jun 13, 2022

The cos-Lindley model with modeling to service times and failure times data

International Journal of Modelling and Simulation, Jul 30, 2023

Exponentiated Discrete Modified Lindley Distribution and its Applications in the Healthcare Sector

CRC Press eBooks, Mar 16, 2023

A Retrospective Study on Skellam and Related Distributions

DOAJ (DOAJ: Directory of Open Access Journals), 2022

This paper reviews works on Skellam distribution, its extensions and areas of applications. Avail... more This paper reviews works on Skellam distribution, its extensions and areas of applications. Available literature shows that this distribution is flexible for modelling integer data where they appear as count data or paired count data in the field of finance, medicine, sports, and science. Bivariate Skellam distribution, dynamic Skellam model and other extensions are also discussed and additional literature are provided.

Odd Exponential-Logarithmic Family of Distributions: Features and Modeling

Mathematical and computational applications, Aug 8, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more

Applications of HLMOL-X Family of Distributions to Time Series, Acceptance Sampling and Stress-strength Parameter

Austrian Journal of Statistics, Jan 25, 2022

In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are... more In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are investigated with special emphasis to the half logistic-Marshall Olkin Lomax distribution. The specific areas we concentrated are time series modeling, acceptance sampling plan and stress-strength analysis. Different autoregressive minification structures of order one are introduced. The acceptance sampling plan is detailed by considering life time of products following the half logistic-Marshall Olkin Lomax distribution. The stress-strength reliability of the half logistic-Marshall Olkin Lomax distribution is derived and estimated. A simulation study is carried out to examine the bias, mean square error, average confidence length and coverage probability of the maximum likelihood estimator of the stress-strength reliability. Finally a real-life data analysis has also been presented.

The Marshall-Olkin Modified Lindley Distribution: Properties and Applications

Journal of reliability and statistical studies, Oct 28, 2020

This article is devoted to a new Marshall-Olkin distribution by using a recent modification of th... more This article is devoted to a new Marshall-Olkin distribution by using a recent modification of the Lindley distribution. Mathematical features of the new model are described. Utilizing maximum likelihood method, the parameters of the new model are estimated. Performance of the estimation approach is discussed by means of a simulation procedure. Moreover, applications of the new distribution are presented which reveal its superiority over other three competing Marshall-Olkin extended distributions of the literature.

A Discrete Kumaraswamy Marshall-Olkin Exponential Distribution

Journal of the Iranian Statistical Society, Dec 1, 2021

Finding new families of distributions has become a popular tool in statistical research. In this ... more Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some important distributions as special cases. Some properties of the new distribution are derived. The model parameters are estimated by the maximum likelihood method, with validation through a complete simulation study. The usefulness of the new model is illustrated via counttype real data sets.

A Statistical Study on Political Awareness among Youngsters in India

Iranian Journal of Educational Sociology

Nowadays, young people are spending the majority of their time on social media, using various pla... more Nowadays, young people are spending the majority of their time on social media, using various platforms like WhatsApp, Facebook, Instagram, etc. It is a common perception that these media have become the new sources of information, which progressively converts into knowledge. It is interesting to check whether they use those sources to achieve knowledge or not. The main focal point of this study is to understand the political engagement, knowledge, and outlook of college-studying youngsters in India. It studies the factors influencing political awareness and examines the influence of politics and politicians on the involvement of youngsters in politics. The findings show that social media has a significant influence on political issues, but they are also more corrupted.

The Inverted Modified Lindley Distribution

Journal of statistical theory and practice, Jun 18, 2020

This paper introduces a new inverted distribution derived from the modified Lindley distribution,... more This paper introduces a new inverted distribution derived from the modified Lindley distribution, and called the inverted modified Lindley. Its properties are derived and parameter is estimated by the methods of moments and maximum likelihood. The nice performance of the obtained estimates is validated by means of a simulation study. The adaptability of the new single parameter model is communicated by using three examples of real data and is depicted graphically.

The Truncated Modified Lindley Generated Family of Distributions

CRC Press eBooks, Mar 16, 2023

A comparative study of various estimation methods for modified Lindley distribution

Biometrics & Biostatistics International Journal, Jul 5, 2022

In this section, we concentrate on the estimation of parameter β , with an assumption that β is u... more In this section, we concentrate on the estimation of parameter β , with an assumption that β is unknown. Here, we consider estimating the parameter of the ML distribution using the methods, which include Maximum Likelihood (ML), Method of Moment (MOM) estimation, least squares (LS) and Weighted Least squares (WLS) estimation, and Cram´er-von Mises (CVM) estimation. ML estimation Consider (y 1 , y 2 , ..., y n) to be a random sample from the ML distribution with parameter β , with pdf defined in Equation (1). The log-likelihood (LL) function is given by The ML estimate of β , β  is defined as

Statistical study on challenges faced by students during lockdown due to COVID-19

Biometrics & Biostatistics International Journal, Dec 24, 2021

Due to the COVID-19 pandemic, the worldwide education system has been rigorously affected, follow... more Due to the COVID-19 pandemic, the worldwide education system has been rigorously affected, following the shutdown of schools and colleges/universities since March 2020 in order to prevent the spread of the virus. Conventional classrooms shifted to online classrooms which profoundly impacted teachers’ and students’ closed interaction, making a paradigm shift in the teaching-learning process. The Covid-19 Pandemic transformed the whole education process to online which has been transited to e-learning in most universities worldwide. The transition to a new environment of education, learners need special social care to improve their concentration and motivation to online learning in such a crucial crisis. The purpose of this study was to look out for the challenges and obstacles encountered in learning during the lockdown and if they were raising the mental stress in students. The study is based on a primary data collected from Kerala, India.

A new modified Lindley distribution with properties and applications

Journal of Statistics and Management Systems, Apr 18, 2021

Abstract This paper introduces a new one-parameter distribution derived from the Lindley distribu... more Abstract This paper introduces a new one-parameter distribution derived from the Lindley distribution, called the modified Lindley distribution. Its main feature is to operate a simple trade-off between the exponential and Lindley distributions, offering an interesting alternative to these two well-established distributions. We study the main properties of the proposed distribution, with a special emphasis on its moments, reliability parameter and asymptotic distributions of the extreme order statistics. Then, inferential considerations are explored. We discuss the parameter estimation by the moments and maximum likelihood methods. Three applications reveal that the new model has the ability to fit well practical data sets.

A retrospective study on Lindley distribution

Biometrics & Biostatistics International Journal, Apr 3, 2018

Generalizations make a distribution more flexible especially for studying the tail properties. Th... more Generalizations make a distribution more flexible especially for studying the tail properties. There exist many generalized family of continuous univariate distributions. In this article, a survey on Lindley distribution, its extensions and classes is conducted. Several available generalizations of the distribution are reviewed and recent trends in the construction of generalized classes are discussed.

Reliability Test Plan for an Extended Birnbaum-Saunders Distribution

Journal of reliability and statistical studies, Jun 22, 2021

Birnbaum-Saunders distribution has been widely studied in statistical literature because this dis... more Birnbaum-Saunders distribution has been widely studied in statistical literature because this distribution accommodates several interesting properties. The purpose of this paper is to introduce a new parametric distribution based on the Birnbaum-Saunders model and develop a new acceptance sampling plans for derived extended Birnbaum-Saunders distribution when the mean lifetime test is truncated at a predetermined time. For various acceptance numbers, confidence levels and values of the ratio of the fixed experimental time to the specified mean life, the minimum sample size necessary to assure a specified mean lifetime worked out. The results are illustrated by a numerical example. The operating characteristic functions of the sampling plans and producer's risk and the ratio of true mean life to a specified mean life that ensures acceptance with a pre-assigned probability are tabulated. This paper presents relevant characteristics of the new distribution and a new acceptance sampling plans when the lifetime of a product adopts an extended Birnbaum-Saunders distribution. Based on this study, the optimal number of testers demanded is decreases as test termination time increases. Moreover, the operating characteristic values increases as the mean life ratio increases,

On a new distribution based on the arccosine function

Arabian Journal of Mathematics, Aug 9, 2021

This note focuses on a new one-parameter unit probability distribution centered around the invers... more This note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be "round mesokurtic" and "left skewed". With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

The Marshall-Olkin Extended Power Lomax Distribution with Applications

Pakistan Journal of Statistics and Operation Research, Jun 3, 2020

In this article, we define a new four-parameter model called Marshall-Olkin extended power Lomax ... more In this article, we define a new four-parameter model called Marshall-Olkin extended power Lomax distribution and study its properties. Limiting distributions of sample maxima and sample minima are derived. The reliability of a system when both stress and strength follows the new distribution is discussed and associated characteristics are computed for a simulated data. Finally, utilizing maximum likelihood estimation, the goodness of the distribution is tested for a real data.

The Weibull Distribution: A Revisit

Abstract Weibull distribution is the most popular model in modeling data from various fields. Fro... more Abstract Weibull distribution is the most popular model in modeling data from various fields. From its introduction, comprehensive work has been done on this model providing distinct interpretations, constructions, generalizations, inferential methods, discrete cases and extensions to bivariate and multivariate. More than 4000 papers have appeared describing all these aspects and developments. This paper provides a review on the historical background and parallel developments of the Weibull distribution. Further, various generalizations and applications of the Weibull distribution are described. Keywords: Bivariate distribution, exponential distribution, hazard rate function, probability density function, Weibull Distribution Cite this Article Jiju Gillariose, Lishamol Tomy. The Weibull Distribution: A Revisit. Research & Reviews: Journal of Statistics. 2020 ; 9(1):16–26p.

A new discrete distribution on integers: Analytical and applied study on stock exchange and flood data

Journal of Statistics and Management Systems, Jul 29, 2022

The Poisson-Lindley difference model with application to discrete stock price change

International Journal of Modelling and Simulation, Jun 13, 2022

The cos-Lindley model with modeling to service times and failure times data

International Journal of Modelling and Simulation, Jul 30, 2023

Exponentiated Discrete Modified Lindley Distribution and its Applications in the Healthcare Sector

CRC Press eBooks, Mar 16, 2023

A Retrospective Study on Skellam and Related Distributions

DOAJ (DOAJ: Directory of Open Access Journals), 2022

This paper reviews works on Skellam distribution, its extensions and areas of applications. Avail... more This paper reviews works on Skellam distribution, its extensions and areas of applications. Available literature shows that this distribution is flexible for modelling integer data where they appear as count data or paired count data in the field of finance, medicine, sports, and science. Bivariate Skellam distribution, dynamic Skellam model and other extensions are also discussed and additional literature are provided.

Odd Exponential-Logarithmic Family of Distributions: Features and Modeling

Mathematical and computational applications, Aug 8, 2022

This article is an open access article distributed under the terms and conditions of the Creative... more

Applications of HLMOL-X Family of Distributions to Time Series, Acceptance Sampling and Stress-strength Parameter

Austrian Journal of Statistics, Jan 25, 2022

In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are... more In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are investigated with special emphasis to the half logistic-Marshall Olkin Lomax distribution. The specific areas we concentrated are time series modeling, acceptance sampling plan and stress-strength analysis. Different autoregressive minification structures of order one are introduced. The acceptance sampling plan is detailed by considering life time of products following the half logistic-Marshall Olkin Lomax distribution. The stress-strength reliability of the half logistic-Marshall Olkin Lomax distribution is derived and estimated. A simulation study is carried out to examine the bias, mean square error, average confidence length and coverage probability of the maximum likelihood estimator of the stress-strength reliability. Finally a real-life data analysis has also been presented.

The Marshall-Olkin Modified Lindley Distribution: Properties and Applications

Journal of reliability and statistical studies, Oct 28, 2020

This article is devoted to a new Marshall-Olkin distribution by using a recent modification of th... more This article is devoted to a new Marshall-Olkin distribution by using a recent modification of the Lindley distribution. Mathematical features of the new model are described. Utilizing maximum likelihood method, the parameters of the new model are estimated. Performance of the estimation approach is discussed by means of a simulation procedure. Moreover, applications of the new distribution are presented which reveal its superiority over other three competing Marshall-Olkin extended distributions of the literature.

A Discrete Kumaraswamy Marshall-Olkin Exponential Distribution

Journal of the Iranian Statistical Society, Dec 1, 2021

Finding new families of distributions has become a popular tool in statistical research. In this ... more Finding new families of distributions has become a popular tool in statistical research. In this article, we introduce a new flexible four-parameter discrete model based on the Marshall-Olkin approach, namely, the discrete Kumaraswamy Marshall-Olkin exponential distribution. The proposed distribution can be viewed as another generalization of the geometric distribution and enfolds some important distributions as special cases. Some properties of the new distribution are derived. The model parameters are estimated by the maximum likelihood method, with validation through a complete simulation study. The usefulness of the new model is illustrated via counttype real data sets.