Borel-Tanner Distribution Research Articles

Applications of Fractional Calculus and Borel Distribution Series for Multivalent Functions on Complex Hilbert Space

In this paper, we introduce applications of fractional calculus techniques for a family of multivalent analytic functions defined by the Borel distribution on Hilbert space. We derive several interesting properties, including coefficient estimates, extreme points, and convex combinations.

Designing of Single Sampling Plan by Attributes Under the Conditions of Borel Distribution

Designing of Single Sampling Plan by Attributes Under the Conditions of Borel Distribution

An application of the Mittag-Leffler-type Borel distribution and Gegenbauer polynomials on a certain subclass of bi-univalent functions

The Mittag-Leffler-type Borel distribution is widely recognized and utilized as a beneficial and pertinent model across numerous applications. This study presents a new subclass of normalized analytic bi-univalent functions that combines Gegenbauer polynomials and the Mittag-Leffler-type Borel distribution. Employing this subclass enables us to derive novel approximations for Taylor-Maclaurin coefficients, |a2| and |a3|, as well as delve into the investigation of the Fekete-Szegö functional. Additionally, we explore a variety of new findings that arise through the specialization of parameters in our primary results.

Some Useful Results on Fuzzy Differential Subordination of Multivalent Functions Defined by Borel Distribution Series

In this work, we define and study some families of multivalent analytic functions defined by the fuzzy subordination and Borel distribution. We discuss some interesting inclusion results and various other useful properties involving integral of these families.

Coefficient Estimate for a Subclass of Close-to-Convex Functions with Respect To Symmetric and Conjugate Points Connected With the Q−Borel Distribution

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Generalising cases of insensitive queuing city traffic management systems and their impact on the delivery of goods by air and road

It is established that the urban traffic management system, as well as the aviation traffic management system, has a significant impact on the multimodal delivery of goods in the road-air transport, which requires the creation of tools for theoretical substantiation and practical implementation. The authors� method of determination the occurrence of vehicles queues in cities using mathematical modelling tools for three scenarios of crossing intersections was developed. The conceptual scheme for calculating the occurrence of the queue of vehicles was proposed. It was noted that vehicles in the queue often arrive randomly, the duration of service is constant, and the probability that before the queue disappears for the first time a certain number of cars cross the intersection has a Borel-Tanner distribution. The given mathematical modelling should become a part of tools for the implementation of the integrated intelligent information system of cities as a cluster of the city traffic management system.

New family of bi-univalent functions with respect to symmetric conjugate points associated with Borel distribution

Abstract In this paper, we introduce and investigate a new family, denoted by 𝒲Σ sc (λ, η, δ, r), of normalized holomorphic and bi-univalent functions with respect to symmetric conjugate points, defined in 𝕌, by making use the Borel distribution series, which is associated with the Horadam polynomials. We derive estimates on the initial Taylor-Maclaurin coefficients and solve the Fekete-Szeg˝o type inequalities for functions in this family.

Outbreak economic analysis of six imported hemorrhagic fevers following detection at 24 hours

Abstract A ten-language search found no economic analysis of symptomatic hemorrhagic fever importation for Crimean Congo (CCHF), Hantavirus (HV), Lassa (LV), Marburg (MARV), Middle East Respiratory Syndrome (MERS) or Nipah (NV) into the USA/EU/UK. This study used available literature to calculate the cost of importation of the six selected fevers with each outbreak detected at 24 hours. A PRISMA search of Pubmed and grey literature was undertaken to uncover respective R0, case fatality ratios, average hospital stay, time to death, frontline casualty frequency and contact histories. A simulated breakout, t24 intervention, Borel distribution contact model, with R0 determined infection (0-1.59) and death rate (CFR: 0.01-0.5) was formed. Treatment inc. plasma therapy, and PPE best prices were determined. ICU median operational costs were factored with contact tracing. Indirect admin costs, based on national mean values, frontline replacement, GNI per capita productivity losses through isolation (21 days as standard), hospitalisation and death were factored. Mean patient discharge ranged 4.4 - 28 days (CCHF to MERS). Time to death ranged 2 - 15 days (HV, NV). The number infected at t48 ranged 1 - 9.59 (CCHF/HV to MARV). Contacts ranged 27 - 169 (CCHF to MARV/NV/MERS). Direct costs of outbreak care, labour, and tracing ranged €424707 - €2850083.07 (CCHF - MARV). Indirect costs, attributed to administrative burdens ranged €5264 -€32800.02 (CCHF to MARV). Productivity losses, attributed separately to the isolated, treated, and dead totaled €2042613 - €26198606 (CCHF - MARV). The total outbreak cost ranged €2488512.78 - €29081489.72 (EU, CCHF - MARV). Significant direct, indirect and productivity costs were attributed to the importation of a single case of six hemorrhagic fevers when detected at t24. The significant societal cost of MARV in particular highlights the importance of continued hemorrhagic fever research and preparedness to healthcare systems in protecting future budgets. Key messages • The importation of hemorrhagic fevers has significant direct and indirect budgetary, and productivity, impacts. • Besides human cost, financial costs demand public health enhanced surveillance and response plans for hemorrhagic fever importation.

Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution

Coefficient estimates for a class of bi-univalent functions involving Mittag-Leffler type Borel distribution

Inclusion Properties of p-Valent Functions Associated with Borel Distribution Functions

In this paper, we define a differential operator on an open unit disk Δ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p-valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on Δ, and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p-univalent functions with BD and offers valuable understanding for further research in complex analysis.

Bell Distribution Series Defined on Subclasses of Bi-Univalent Functions That Are Subordinate to Horadam Polynomials

Several different subclasses of the bi-univalent function class Σ were introduced and studied by many authors using distribution series like Pascal distribution, Poisson distribution, Borel distribution, the Mittag-Leffler-type Borel distribution, Miller–Ross-Type Poisson Distribution. In the present paper, by making use of the Bell distribution, we introduce and investigate a new family GΣt(x,p,q,λ,β,γ) of normalized bi-univalent functions in the open unit disk U, which are associated with the Horadam polynomials and estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to this class. Furthermore, we establish the Fekete–Szegö inequality for functions in the family GΣt(x,p,q,λ,β,γ). After specializing the parameters used in our main results, a number of new results are demonstrated to follow.

Applications of Gegenbauer Polynomials for Subfamilies of Bi-Univalent Functions Involving a Borel Distribution-Type Mittag-Leffler Function

In this research, a novel linear operator involving the Borel distribution and Mittag-Leffler functions is introduced using Hadamard products or convolutions. This operator is utilized to develop new subfamilies of bi-univalent functions via the principle of subordination with Gegenbauer orthogonal polynomials. The investigation also focuses on the estimation of the coefficients |aℓ|(ℓ=2,3) and the Fekete–Szegö inequality for functions belonging to these subfamilies of bi-univalent functions. Several corollaries and implications of the findings are discussed. Overall, this study presents a new approach for constructing bi-univalent functions and provides valuable insights for further research in this area.

Some Structural Properties Related to the Borel-Taner Distribution and its’ Application

The Borel-Tanner distribution, with two shape parameters, and r, has some leverage over the Poisson distribution, other mixtures of the Poisson distribution, and several other discrete distributions, as it can be applied to both under and over-dispersed count data. In this article, some structural properties are studied that have not been explored earlier including recursive relation between successive probabilities. For illustrative purposes, two real-life data sets will be considered to show the applicability of this distribution that are re-analyzed for this purpose.

Toeplitz Determinants for a Certain Family of Analytic Functions Endowed with Borel Distribution

In this work, we derive coefficient bounds for the symmetric Toeplitz matrices T2(2), T2(3), T3(1), and T3(2), which are the known first four determinants for a new family of analytic functions with Borel distribution series in the open unit disk U. Further, some special cases of results obtained are also pointed.

Properties of analytic functions associated with Mitttag-Leffler-type Borel distribution series

Keeping in view of the latest trends toward special functions, due its various applications in Physics and applied Mathematics, we introduce a subclass of analytic functions with the help of Borel distribution series. Furthermore, we investigate some useful geometric and algebric properties of these functions. We discuss coefficient estimates, growth and distortion theorems, radii of close-to-convexity, starlikeness, convexity and convolution properties to this subclass. subject classification numbers as needed.

A Certain Subclass of Multivalent Functions Associated with Borel Distribution Series

In this paper, we determine the necessary and sufficient conditions for the power series f(z) whose coefficients are probabilities of the Borel distribution to be in the family J(p,λ ,α,β,γ) of analytic functions which defined in the open unit disk. We derive a number of important geometric properties, such as, coefficient estimates, integral representation, radii of starlikeness and convexity. Also we discuss the extreme points and neighborhood property for functions belongs to this family.

Certain Subclasses of Analytic Functions Associated with Generalized Telephone Numbers

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality for f in the new function class. Comparable results have been attained for the function f−1. Further application of our outcomes to certain functions demarcated by convolution products with certain normalized analytic functions in the open unit disk are specified, and we obtain Fekete–Szegö variations for this new function class defined over Poisson and Borel distribution series.

On Subclasses of Uniformly Convex Spriallike Function Associated with Poisson Distribution Series

Geometric Function Theory is one of the major area of mathematics which suggests the significance of geometric ideas and problems in complex analysis. Recently, the univalent functions are given particular attention and they are used to construct linear operators that preserve the class of univalent functions and some of its subclasses. Also, similar attention has been given to distribution series. Many authors have studied about certain subclasses of univalent and bi-univalent functions connected with distribution series like Pascal distribution, Binomial distribution, Poisson distribution, Mittag-Leffler-type Poisson distribution, Geometric distribution, Exponential distribution, Borel distribution, Generalized distribution and Generalized discrete probability distribution to name few. Some of the important results on Uniformly convex spirallike functions (UCF) and Uniformly spirallike functions (USF) related with such a distribution series are also of interest. The main aim of the present investigation is to obtain the necessary and sufficient conditions for Poisson distribution series to belong to the classes <img src=image/13427077_01.gif> and <img src=image/13427077_02.gif>. The inclusion properties associated with Poisson distribution series are taken up for study in this article. Proof of some inequalities on integral function connected to Poisson distribution series has also been discussed. Further, some corollaries and results that follow consequently from the theorems are also analysed.

Zero-inflated Modified Borel-Tanner Regression Model for Count Data

By starting from the one-parameter Modified Borel-Tanner distribution proposed recently in the statistic literature, we introduce the zero-inflated Modified Borel-Tanner distribution. Additionally, on the basis of the proposed zero-inflated distribution, a novel zero-inflated regression model is proposed, which is quite simple and may be an interesting alternative to usual zero-inflated regression models for count data. The parameters of the proposed model are estimated by Maximum Likelihood Estimation technique. To check the potentiality of the zero inflated Modified Borel-Tanner regression, an application to the count of infected blood cells is taken. The results suggest that the new zero inflated Modified Borel-Tanner regression is more appropriate to model these count data than other familiar zero-inflated (or not) regression models commonly used in practice.

Some properties of analytical functions related to Borel distribution series

In this paper, we introduce and study a new subclass of analytic functions which are defined by means of a linear operator. Some results connected to coefficient estimates, growth and distortion theorems, radii of starlikeness, convexity close-to-convexity and integral means inequalities related to the subclass is obtained.