The use of discrete probabilistic distributions is relevant to many practical tasks, especially in present-day situations where the data on distribution are insufficient and expert knowledge and evaluations are the only instruments for the restoratio...
A subject of this study is the behavior of the tail of the binomial distribution in the case of the Poisson approximation. The deviation from unit of the ratio of the tail of the binomial distribution and that of the Poisson distribution, multiplied...
In this paper, we propose an alternative distribution to model count data exhibiting uni/bimodality. It arises as a weighted version of the beta-binomial distribution, which is defined by a parametric weight function that admits up to two modes for t...
The increase in available probabilistic information and its usefulness for understanding the world has made it necessary to promote probabilistic literate citizens. For this, the binomial distribution is fundamental as one of the most important distr...
The competencies that today’s citizen must possess have led to a transformation of the teaching of probability, which has been repositioned on the school curriculum from an algorithmic view to a practical one based on the understanding of the c...
The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series...
When modeling real-world data, we face the challenge of determining which probability distribution best represents the data. To address this intricate problem, we rely on goodness-of-fit tests. However, when the data come from a bivariate negative bi...
Many decision-making situations require the evaluation of several voters or agents. In a situation where voters evaluate candidates, the question arises of how best to aggregate evaluations so as to compare the candidates. The aim of this work is to...
Inhomogeneous random graphs are commonly used models for complex networks where nodes have varying degrees of connectivity. Computing the degree distribution of such networks is a fundamental problem and has important applications in various fields....
The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the classical de Moivre–Laplace normal approximation in order to give an estimate at the tail as well...
There has been a considerable amount of literature on binomial regression models that utilize well-known link functions, such as logistic, probit, and complementary log-log functions. The conventional binomial model is focused only on a single parame...
The importance of Lagrangian distributions and their applicability in real-world events have been highlighted in several studies. In light of this, we create a new zero-truncated Lagrangian distribution. It is presented as a generalization of the zer...
Statistical and artificial neural network models are applied to forecast the quantum scheme of a three-level atomic system (3LAS) and field, initially following a photon added negative binomial distribution (PANBD). The Mandel parameter is used to de...
In the present paper, due to beta negative binomial distribution series and Laguerre polynomials, we investigate a new family
The competing risk model based on Lindley distribution is discussed under the progressive type-II censored sample data with binomial removals. The maximum likelihood estimation of the unknown parameters of the distribution is established. Using the L...
A new class of distribution called the Fréchet binomial (FB) distribution is proposed. The new suggested model is very flexible because its probability density function can be unimodal, decreasing and skewed to the right. Furthermore, the haza...
This paper investigates the approximated arbitrage bounds of option prices in an incomplete market setting and draws implications for option pricing and risk management. It gives consideration to periods of global financial crisis and European sovere...
In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for...
We discuss a model of seismic activity that is based on the concept of energy in a cluster of sources of seismic activity. We show that specific cases of the studied model lead to the Gutenberg–Richter relationship and the Omori law. These laws...
This study investigates a two-stage production–inventory model with subsidy policies for paper cup recycling. The model includes remanufacturers, recyclers, and consumers, taking into account their preferences for different recycling channels....
When collecting experimental data, the observable may be dichotomous. Sampling (eventually with replacement) thus emulates a Bernoulli trial leading to a binomial proportion. Because the binomial distribution is discrete, the analytical evaluation of...
In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate fun...
Medical studies often involve a comparison between two outcomes, each collected from a sample. The probability associated with, and confidence in the result of the study is of most importance, since one may argue that having been wrong with a percent...
Mathematical models are proposed for statistical regularities of maximum daily precipitation within a wet period and total precipitation volume per wet period. The proposed models are based on the generalized negative binomial (GNB) distribution of t...
In this paper, a new discrete distribution called Binomial–Natural Discrete Lindley distribution is proposed by compounding the binomial and natural discrete Lindley distributions. Some properties of the distribution are discussed including the...
In the statistical literature, one of the most important subjects that is commonly used is stress–strength reliability, which is defined as
We investigate Metropolis–Hastings (MH) algorithms to approximate the distribution of independent binomial random variables conditioned on the sum. Let
The application of microgrids (MG) is more and more extensive, therefore it is important to improve the system management method of microgrids. The intended costs can be further minimized when the energy management system is unified with demand side...
The quadratic unconstrained binary optimization (QUBO) problem is categorized as an NP-hard combinatorial optimization problem. The variable neighborhood search (VNS) algorithm is one of the leading algorithms used to solve QUBO problems. As neighbor...
This article explores how literary features are statistically distributed in the Christian apostle Paul’s letters. While several decades of occasional research have applied statistics to Paul’s letters, most if not all previous such appro...
A new four-parameter lifetime distribution called the beta binomial exponential 2
A class of power series q-distributions, generated by considering a q-Taylor expansion of a parametric function into powers of the parameter, is discussed. Its q-factorial moments are obtained in terms of q-derivatives of its series (parametric) func...
Traditional reliability methods using fixed removal plans often overlook withdrawal randomness, leading to biased estimates for asymmetric data. This study advances classical and Bayesian frameworks for the inverse Chen distribution, which is suited...
We investigate the proximity in terms of zeta-structured metrics of generalized negative binomial random sums to generalized gamma distribution with the corresponding parameters, extending thus the zeta-structured estimates of the rate of convergence...
Process capability and performance indices (PCIs and PPIs) are used in industry to provide numerical measures for the capability and performance of several processes. The majority of the literature refers to PCIs and PPIs for continuous data. The aim...
The chain length distribution (CLD) of a reversible deactivation radical polymerization at full conversion is shown to be a negative binomial distribution with parameters that are simple functions of the number-average degree of polymerization and ei...
The decapod fauna in the intertidal zone of the rocky shores of Chile is highly diverse, especially along the northern and central mainland coasts, where the influence of the cold Humboldt Current results in high productivity. One of the most abundan...
The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad...
In this article, we propose the discrete version of the binomial exponential II distribution for modelling count data. Some of its statistical properties including hazard rate function, mode, moments, skewness, kurtosis, and index of dispersion are d...
This study investigates how the priority rankings for dam construction sites vary with multi-criteria decision making (MCDM) techniques and generation approaches for incomplete information. Strategic environmental assessment (SEA) seeks to recommend...
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these ne...
In this study, we introduce a novel estimation technique for assessing the reliability parameter
Space–time prisms are used to model the uncertainty of space–time locations of moving objects between (for instance, GPS-measured) sample points. However, not all space–time points in a prism are equally likely and we propose a simple, formal model f...
This article completes our studies on the formal construction of asymptotic approximations for statistics based on a random number of observations. Second order Chebyshev–Edgeworth expansions of asymptotically normally or chi-squared distribute...
Frequency analysis of tornadoes is very important for risk analysis and disaster control. In this paper, the annual frequency of tornadoes that occurred in the United States from 1967 to 2016 is analyzed. The simple analysis shows that frequencies of...
In survival analysis, the presence of elements not susceptible to the event of interest is very common. These elements lead to what is called a fraction cure, cure rate, or even long-term survivors. In this paper, we propose a unified approach using...
Pascal’s triangle is a classical mathematical construct, historically studied for centuries, that organises binomial coefficients in a triangular array and serves as a cornerstone in combinatorics, algebra, and number theory. Herein, we propose...
We study classification of random sequences of characters selected from a given alphabet into two classes characterized by distinct character selection probabilities and length distributions. The classification is based on the sign of the log-likelih...
The hypergeometric distribution has gained its importance in practice as it pertains to sampling without replacement from a finite population. It has been used to estimate the population size of rare species in ecology, discrete failure rate in relia...
From Kemp [1], we have a family of confluent q-Chu- Vandermonde distributions, consisted by three members I, II and III, interpreted as a family of q-steady-state distributions from Markov chains. In this article, we provide the moments of the distri...
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