New Results and Matrix Representation for Daehee and Bernoulli Numbers and Polynomials

In this paper, we derive new matrix representation for Daehee numbers and polynomials, the lambda-Daehee numbers and polynomials and the twisted Daehee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on Daehee numbers and polynomials. Moreover, we obtained some new results for Daehee and Bernoulli numbers and polynomials

New Results on Higher-Order Daehee and Bernoulli Numbers and Polynomials

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and short proofs of many previous results on higher order Daehee numbers and polynomials. Moreover, we obtained recurrence relation, explicit formulas and some new results for these numbers and polynomials. Furthermore, we investigated the relation between these numbers and polynomials and Stirling numbers, Norlund and Bernoulli numbers of higher order. The results of this article gives a generalization of the results derived very recently by El-Desouky and Mustafa [6]

A New Extension of Power Hazard Distribution with Applications

A new lifetime distribution is suggested using the Sine function by considering power hazard distribution as baseline distribution. Some mathematical and statistical features are discussed. The Maximum likelihood method is used to estimate the parameters for proposed distribution. Three real data sets are examined to analyze the performance of proposed distribution with some other distributions. The new distribution has been shown better fit to the bladder cancer patients’ data and COVID-19 data as compared to some distributions through statistical criterion

Extended Power Hazard Rate Distribution and its Application

A new model four-parameter model called the odd generalized exponential power hazard rate (OGE-PHR) distribution has been introduced. Some statistical properties for OGE-PHR are obtained. The moments, quantile, mode, reliability, and order statistics are discussed. Estimation of parameters, maximum likelihood technique is employed. Two real data sets are discussed with applications. (original abstract