We study the asymptotic theory of nonparametric estimation of the term structure’s volatility for a class of one factor Heath-Jarrow-Morton term structure models driven by fractional Levy processes. This class of models is important, as it captures, as a
special case, all term structure models where the short term interest rate represents a time-homogeneous univariate fractional diffusion with jumps in the equivalent risk neutral economy.

KEYWORDS: Heath-Jarrow-Morton term structure model, forward rate, fractional Levy process, semimartingale, non-Markov property, hyperbolic Levy motion, jumps, heavy tails, long memory, yield curve, stochastic volatility, kernel estimate, local time,
occupation time, Ito-Tanaka formula, Monte Carlo, particle filtering.

AMS Subject Classification: 60F05; 60F25; 60E05; 60G15; 60G18; 60G22; 60H05; 60H10; 60H35; 60J60; 62F12; 62M09; 62P05; 65C30; 91G20; 91G30.

In the present paper Shannon’s Inequality and its two generalizations are defined. Two new generalized mean code word lengths are introduced and their bounds in terms of the generalized measures of entropies are studied by applying the new two generalizations of Shannon’s inequality thus obtained. Particular cases are also discussed with a list of references in the end.

KEYWORDS: Shannon’s inequality; Codeword length; Source Coding; Holder’s inequality; Kraft inequality.

Cricketing knowledge tells us that batting is more difficult early in a player’s innings but becomes easier as a player familiarizes themselves with the conditions. A comprehensive dataset of T20 matches is utilized to study the impact of different factors
on the survival of batsmen in the highly dynamic and fast-paced T20 format. Survival analysis, in the context of T20, models dismissal as an event. Each batsman’s innings represents a ”lifetime” until dismissal occurs. This research compares the effectiveness of Non-Parametric, Semiparametric, and Parametric survival analysis methods using T20 data. This analysis utilizes several survival models, including the Kaplan-Meier method for estimating survival rates, the Log-rank test for comparing
survival differences between groups, and the Cox Proportional Hazards model for calculating hazard ratios. Additionally, AIC and BIC values were employed to identify the most appropriate survival distribution for each player, which was then applied into a parametric regression model to generate time ratios for each group. Furthermore, Conditional Survival Probabilities can be beneficial for team management in determining or adjusting the batting order during a match based on the current game situation and the opposing team. World’s top eight T20 run scorer Batsmen up to May 31st, 2024, was taken from www.espncricinfo.com for this study. For this analysis carried out from the R Programming Language and its packages like ”survival” and ”surviminer” were used.

KEYWORDS: Survival Analysis; Non-Parametric; Semiparametric; Parametric models; Conditional Survival Probability

In this study, we introduce a size biased version of the negative binomial distribution named as generalized size biased negative binomial distribution and demonstrate its applicability by fitting it to COVID-19 data sets. We derive several key properties of the distribution, including the probability generating function, cumulative distribution function, survival and hazard rate functions, along with recurrence relations for probabilities. Additionally, we explore parameter estimation methods and develop statistical tests to assess the significance of the distribution’s parameters. Furthermore, a simulation study is conducted to evaluate the performance of the parameter estimators obtained using the maximum likelihood method. 

KEYWORDS: count data modeling; maximum likelihood estimation; MCMC simulation; model selection; negative binomial distribution; size biased model; survival function.

Heart disease remains one of the leading causes of morbidity and mortality worldwide, affecting millions of people each year (World Health Organization, 2023). It encompasses various cardiovascular conditions, including coronary artery disease
(CAD), heart failure, and arrhythmias, with CAD being the most prevalent. Early detection and prevention play a crucial role in reducing the burden of heart disease. Traditional diagnostic methods rely on clinical assessments and patient history, but
advancements in artificial intelligence (AI) and machine learning (ML) have enabled more accurate and efficient heart disease prediction. By analyzing multiple risk factors such as blood pressure, cholesterol levels, lifestyle habits, and genetic predisposition, predictive models help in early diagnosis, personalized treatment, and reducing healthcare costs. This article explores the significance of heart disease prediction, highlighting the role of ML-algoriths in improving cardiovascular healthcare. This paper compares eight machine learning algorithms in order to improve predictive accuracy and offer a reliable instrument for early diagnosis. We have compared the following models: Artificial Neural Network (ANN), Decision Tree (DT), K-Nearest Neighbor (KNN), Naive Bayes (NB), Support Vector Machine (SVM), Random Forest (RF), Gradient Boosting (GB) and AdaBoost, using a dataset of 270 patients representing 14 clinical and demographic attributes from the University
of California Irvine’s Machine Learning Repository. The Artificial Neural Network model obtained the highest accuracy at 96.67%, with a precision of 100%, recall of 91.67%, and F1 score of 95.65%. These results underscore the potential of machine
learning algorithms to enhance the early diagnosis of heart disease, thereby assisting healthcare professionals in making better decisions.

KEYWORDS: Heart Disease Prediction, Machine Learning, Artificial Neural Network, Decision Tree, K-Nearest Neighbors, Naive Bayes, Support Vector Machine, Random Forest, Gradient Boosting, AdaBoost.