Ashok Kumar Pathak
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View article: Dependence and Uncertainty: Information Measures using Tsallis Entropy
Dependence and Uncertainty: Information Measures using Tsallis Entropy Open
In multivariate analysis, uncertainty arises from two sources: the marginal distributions of the variables and their dependence structure. Quantifying the dependence structure is crucial, as it provides valuable insights into the relations…
View article: Fractional counting process at Lévy times and its applications
Fractional counting process at Lévy times and its applications Open
Traditionally, fractional counting processes, such as the fractional Poisson process, etc. have been defined using fractional differential and integral operators. Recently, Laskin (2024) introduced a generalized fractional counting process…
View article: Robust and Efficient Fine-tuning of LLMs with Bayesian Reparameterization of Low-Rank Adaptation
Robust and Efficient Fine-tuning of LLMs with Bayesian Reparameterization of Low-Rank Adaptation Open
Large Language Models (LLMs) are highly resource-intensive to fine-tune due to their enormous size. While low-rank adaptation is a prominent parameter-efficient fine-tuning approach, it suffers from sensitivity to hyperparameter choices, l…
View article: Tempered space-time fractional negative binomial process
Tempered space-time fractional negative binomial process Open
In this paper, we define a tempered space-time fractional negative binomial process (TSTFNBP) by subordinating the fractional Poisson process with an independent tempered Mittag-Leffler Lévy subordinator. We study its distributional proper…
View article: Parametric and semiparametric approaches for copula-based regression estimation
Parametric and semiparametric approaches for copula-based regression estimation Open
Based on the normality assumption on dependent variable, regression analysis is one of the most popular statistical techniques for studying the dependence between response and explanatory variables. However, violation of this assumption in…
View article: Multivariate Information Measures: A Copula-based Approach
Multivariate Information Measures: A Copula-based Approach Open
Multivariate datasets are common in various real-world applications. Recently, copulas have received significant attention for modeling dependencies among random variables. A copula-based information measure is required to quantify the unc…
View article: Copula-Based Estimation of Causal Effects in Multiple Linear and Path Analysis Models
Copula-Based Estimation of Causal Effects in Multiple Linear and Path Analysis Models Open
Regression analysis is one of the most popularly used statistical technique which only measures the direct effect of independent variables on dependent variable. Path analysis looks for both direct and indirect effects of independent varia…
View article: Elemental analysis and metabolic profiling of medicinally potent members of Zingiberaceae family using FT-IR and LIBS coupled with PLS-DA
Elemental analysis and metabolic profiling of medicinally potent members of Zingiberaceae family using FT-IR and LIBS coupled with PLS-DA Open
The role of organic and inorganic elemental profiles in the growth, development, and secondary metabolite synthesis of plants is crucial, particularly concerning their medicinal value. However, comprehensive studies addressing both aspects…
View article: Bivariate tempered space-fractional Poisson process and shock models
Bivariate tempered space-fractional Poisson process and shock models Open
We introduce a bivariate tempered space-fractional Poisson process (BTSFPP) by time-changing the bivariate Poisson process with an independent tempered $\alpha$ -stable subordinator. We study its distributional properties and its connectio…
View article: Multivariate Tempered Space-Fractional Negative Binomial Process and Risk Models with Shocks
Multivariate Tempered Space-Fractional Negative Binomial Process and Risk Models with Shocks Open
In this paper, we first define the multivariate tempered space-fractional Poisson process (MTSFPP) by time-changing the multivariate Poisson process with an independent tempered α-stable subordinator. Its distributional properties, the mix…
View article: On Generalized Transmuted Lifetime Distribution
On Generalized Transmuted Lifetime Distribution Open
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution func…
View article: Record-based transmuted unit omega distribution: different methods of estimation and applications
Record-based transmuted unit omega distribution: different methods of estimation and applications Open
Dombi et al. (2019) introduced a three parameter omega distribution and showed that its asymptotic distribution is the Weibull model. We propose a new record-based transmuted generalization of the unit omega distribution by considering Bal…
View article: A Probabilistic Extension of the Fubini Polynomials
A Probabilistic Extension of the Fubini Polynomials Open
In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral repres…
View article: Serous macular detachment in a case of posterior microphthalmos: A rare manifestation of pachychoroid spectrum
Serous macular detachment in a case of posterior microphthalmos: A rare manifestation of pachychoroid spectrum Open
A 22-year-old male patient presented with sudden severe diminution of vision in the right eye (RE) for 1 day which was associated with flashes and floaters. He was eventually diagnosed to have posterior microphthalmos with serous macular d…
View article: Bivariate Tempered Space-Fractional Poisson Process and Shock Models
Bivariate Tempered Space-Fractional Poisson Process and Shock Models Open
In this paper, we introduce a bivariate tempered space-fractional Poisson process (BTSFPP) by time-changing the bivariate Poisson process with an independent tempered $α$-stable subordinator. We study its distributional properties and its …
View article: A Novel Bivariate Generalized Weibull Distribution with Properties and Applications
A Novel Bivariate Generalized Weibull Distribution with Properties and Applications Open
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 univa…
View article: Generalized Fractional Negative Binomial Process
Generalized Fractional Negative Binomial Process Open
In this paper, we introduce a generalized fractional negative binomial process (GFNBP) by time changing the fractional Poisson process with an independent Mittag-Leffler (ML) Levy subordinator. We study its distributional properties and it…
View article: A new class of copulas having dependence range larger than FGM-type copulas
A new class of copulas having dependence range larger than FGM-type copulas Open
We propose a new bivariate symmetric copula with positive and negative dependence properties. The main features of the proposed copula are its simple mathematical structure, wider dependence range compared to FGM copula and its generalizat…
View article: Effect of Timing of Pars Plana Vitrectomy on Visual Outcome in Cases of Nucleus Drop during Phacoemulsification
Effect of Timing of Pars Plana Vitrectomy on Visual Outcome in Cases of Nucleus Drop during Phacoemulsification Open
PURPOSE: The purpose of the study was to study the relationship between the timing of pars plana vitrectomy (PPV) with corrected distance visual acuity (CDVA) in cases of nucleus drop during phacoemulsification. METHODS: This retrospective…
View article: Moderation effects of serotype on dengue severity across pregnancy status in Mexico
Moderation effects of serotype on dengue severity across pregnancy status in Mexico Open
View article: Severe ocular involvement in ecthyma gangrenosum
Severe ocular involvement in ecthyma gangrenosum Open
Ecthyma Gangrenosum (EG) is a cutaneous infection occurring mainly in immunocompromised patients with very rare ocular involvement. We report a rare case of an immunocompetent, 16 year old female with bilateral pseudomembranous conjunctivi…
View article: Management of Ciliary Staphyloma as a Complication of Silicone Oil Infusion During Retinal Detachment Surgery - A Case Report
Management of Ciliary Staphyloma as a Complication of Silicone Oil Infusion During Retinal Detachment Surgery - A Case Report Open
Silicone oil infusion is a frequently used modality for intraocular tamponade in various vitreoretinal surgeries.This surgical tool is by and large safe and effective but is associated with various complications like raised intraocular pre…
View article: Innovative Investigation of Zinc Oxide Nanoparticles Used in Dentistry
Innovative Investigation of Zinc Oxide Nanoparticles Used in Dentistry Open
Dental caries is a major lifestyle concern as dental components affect the face of an individual. The issue of tooth decay occurs in every age group throughout the globe. Researchers are probing incipient implements and techniques to devel…
View article: Estimation after selection from bivariate normal population with application to poultry feeds data
Estimation after selection from bivariate normal population with application to poultry feeds data Open
In many practical situations, it is often desired to select a population (treatment, product, technology, etc.) from a choice of several populations on the basis of a particular characteristic that associated with each population, and then…
View article: Discussion on a new extension of the FGM copula with application in reliability
Discussion on a new extension of the FGM copula with application in reliability Open
A new extended Farlie-Gumbel-Morgenstern copula recently studied by Ebaid et al. [Comm. Statist. Theory Methods, (2020)] is reviewed. The reported admissible range for the copula parameter a is incorrect and some typos are also found in th…
View article: Fate of indeterminate microbial keratitis
Fate of indeterminate microbial keratitis Open
Background: Previous published literature has shown that there is no significant difference between outcomes of culture positive and culture negative infective keratitis. This study was done to find the outcome in cases of indeterminate ke…
View article: COVID-19 Vaccine Hesitancy and Emerging Variants: Evidence from Six Countries
COVID-19 Vaccine Hesitancy and Emerging Variants: Evidence from Six Countries Open
As the world tries to cope with the devastating effects of the COVID-19 pandemic and emerging variants of the virus, COVID-19 vaccination has become an even more critical tool toward normalcy. The effectiveness of the vaccination program a…
View article: Impact of Environmental Indicators on the COVID-19 Pandemic in Delhi, India
Impact of Environmental Indicators on the COVID-19 Pandemic in Delhi, India Open
Currently, there is a massive debate on whether meteorological and air quality parameters play a crucial role in the transmission of COVID-19 across the globe. With this background, this study aims to evaluate the impact of air pollutants …
View article: A Novel Bivariate Generalized Weibull Distribution with Properties and Applications
A Novel Bivariate Generalized Weibull Distribution with Properties and Applications Open
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 univa…