A new class of score generating functions for regression models

2002 ◽  
Vol 57 (2) ◽  
pp. 205-214 ◽  
Author(s):  
Young Hun Choi ◽  
Ömer Öztürk
Keyword(s):  
Generating Functions ◽  
Regression Models ◽  
New Class

scholarly journals A New Class of Laguerre-based Generalized Apostol Polynomials

2016 ◽  
Vol 57 (1) ◽  
pp. 67-89 ◽  
Author(s):  
N.U. Khan ◽  
T. Usman
Keyword(s):  
Generating Functions ◽  
General Symmetry ◽  
Genocchi Numbers ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae

Abstract In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.

scholarly journals Multifarious Results for q-Hermite Based Frobenius Type Eulerian Polynomials

2019 ◽  
Author(s):  
Waseem Khan ◽  
Idrees Ahmad Khan ◽  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Series Representation ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Eulerian Polynomials ◽  
New Class ◽  
Genocchi Polynomials

In this paper, a new class of q-Hermite based Frobenius type Eulerian polynomials is introduced by means of generating function and series representation. Several fundamental formulas and recurrence relations for these polynomials are derived via different generating methods. Furthermore, diverse correlations including the q-Apostol-Bernoulli polynomials, the q-Apostol-Euler poynoomials, the q-Apostol-Genocchi polynomials and the q-Stirling numbers of the second kind are also established by means of the their generating functions.

scholarly journals A New Class of Hermite-Fubini Polynomials and Its Properties

2019 ◽  
Author(s):  
Waseem Khan ◽  
Nisar K S
Keyword(s):  
Generating Functions ◽  
New Class ◽  
Summation Formulas ◽  
Symmetric Identities

In this paper, we introduce a new class of Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of Hermite-Fubini numbers and polynomials by using generating functions.

A new class of regression model for a bounded response with application in the study of the incidence rate of colorectal cancer

2019 ◽  
Vol 29 (7) ◽  
pp. 2015-2033
Author(s):  
Vicente G Cancho ◽  
Jorge L Bazán ◽  
Dipak K Dey
Keyword(s):  
Colorectal Cancer ◽  
Regression Model ◽  
Incidence Rate ◽  
Regression Models ◽  
Real Data ◽  
Unit Interval ◽  
Open Unit ◽  
Medical Sciences ◽  
New Class ◽  
New Family

Response variables in medical sciences are often bounded, e.g. proportions, rates or fractions of incidence of some disease. In this work, we are interested to study if some characteristics of the population, e.g. sex and race which can explain the incidence rate of colorectal cancer cases. To accommodate such responses, we propose a new class of regression models for bounded response by considering a new distribution in the open unit interval which includes a new parameter to make a more flexible distribution. The proposal is to obtain compound power normal distribution as a base distribution with a quantile transformation of another family of distributions with the same support and then is to study some properties of the new family. In addition, the new family is extended to regression models as an alternative to the regression model with a unit interval response. We also present inferential procedures based on the Bayesian methodology, specifically a Metropolis–Hastings algorithm is used to obtain the Bayesian estimates of parameters. An application to real data to illustrate the use of the new family is considered.

scholarly journals On generating functions for classical polynomials

1973 ◽  
Vol 15 (4) ◽  
pp. 389-392
Author(s):  
O. Shanker
Keyword(s):  
Generating Functions ◽  
New Class ◽  
Classical Polynomials

Recently Brown [1] gave two new classes of generating functions which include the generating functions for the polynomials of Gegenbauer, Jacobi and Laguerre. The aim of the paper is to give a new class of generating functions which includes both sets of generating functions given by Brown and provides a new class of generating functions for the polynomials of Gegenbauer, Jacobi and Laguerre.

A new class of multivariate skew distributions with applications to Bayesian regression models

2009 ◽  
Vol 37 (2) ◽  
pp. 301-302 ◽  
Author(s):  
Sujit K. Sahu ◽  
Dipak K. Dey ◽  
Márcia D. Branco
Keyword(s):  
Regression Models ◽  
Bayesian Regression ◽  
Skew Distributions ◽  
New Class

On Generating Functions for a New Class of Polynomials

1971 ◽  
Vol 51 (1-6) ◽  
pp. 43-58 ◽  
Author(s):  
K. C. Gupta ◽  
S. P. Goyal
Keyword(s):  
Generating Functions ◽  
New Class

scholarly journals New classes of recurrence relations involving hyperbolic functions, special numbers and polynomials

2021 ◽  
pp. 15-15
Author(s):  
Yilmaz Simsek
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Umbral Calculus ◽  
Discrete Mathematics ◽  
New Class ◽  
Integral Formulas ◽  
Euler Numbers And Polynomials ◽  
Derivative Formulas ◽  
Special Numbers And Polynomials

By using the calculus of finite differences methods and the umbral calculus, we construct recurrence relations for a new class of special numbers. Using this recurrence relation, we define generating functions for this class of special numbers and also new classes of special polynomials. We investigate some properties of these generating functions. By using these generating functions with their functional equations, we obtain many new and interesting identities and relations related to these classes of special numbers and polynomials, the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Stirling numbers. Finally, some derivative formulas and integral formulas for these classes of special numbers and polynomials are given. In general, this article includes results that have the potential to be used in areas such as discrete mathematics, combinatorics analysis and their applications.

scholarly journals A Note on Degenerate Hermite-Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem A. Khan ◽  
Idrees A. Khan ◽  
Nisar K S
Keyword(s):  
Generating Functions ◽  
New Class ◽  
Summation Formulas ◽  
Symmetric Identities

In this paper, we introduce a new class of degenerate Hermite-Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we derive symmetric identities of degenerate Hermite-Fubini numbers and polynomials by using generating functions.

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