New polynomial exponential distribution: properties and applications

The paper investigates a nonlinear model that describes population dynamics with an age structure. The fertility rate, which varies with age, follows a nonconstant pattern. The model exhibits a multiplicative structure for both fertility and mortality rates. Remarkably, this multiplicative structure renders the model separable. In this setting, it is shown that the number of births in unit time can be expressed using a system of nonlinear ordinary differential equations. The asymptotic behavior of solutions to this system has been established for a specific case. This result is significant because it provides a mathematical framework for understanding the dynamics of birth rates in certain settings. Furthermore, this paper explicitly identifies the steady-state solution and the equilibrium solution. As in any research paper, new directions of study remain open.

“…Inspired by [17][18][19], recent work [20] considers a model with a pseudo-exponential survival probability π(a), i.e.,…”

Section: A Special Linear Population Modelmentioning

confidence: 99%

“…Finally, we point out that in [17] a new polynomial exponential family is introduced. The study investigates its density, hazard rate functions, numerical properties, and applications to real-world datasets.…”

Section: Some Remarksmentioning

confidence: 99%

The Equilibrium Solutions for a Nonlinear Separable Population Model

Covei,

Pirvu,

Sterbeti

2024

“…As time progresses, more and more probability distributions are published, which (albeit mostly at the cost of complexity) better describe the specifics of data sets obtained under specific conditions. For example, very promising modifications of the decadesknown Lindley distribution have been published recently, in particular the XLindley and power XLindlay distributions [25][26][27]. Among the enormous number of different new distributions, there would likely be some that would prove useful in some of the specific cases studied in this article.…”

Section: Final Commentmentioning

confidence: 99%

Four-Parameter Weibull Distribution with Lower and Upper Limits Applicable in Reliability Studies and Materials Testing

Kohout

2023

A simply curved Weibull plot means that the studied data set has a three-parameter Weibull distribution with a non-zero location parameter representing the lower or the upper limit of the data set. This paper introduces a four-parameter Weibull distribution with both of these limits that can be applied in both reliability and materials engineering. A very reliable indicator of this distribution is the double-curved Weibull plot. The great advantage of this distribution is the fact that the corresponding hazard rate curve can be bathtub-shaped with a great ability to fit the measured data.

“…The NXL distribution is a special case of one-parameter polynomial exponential distribution (NPED) proposed in [22]. The probability density function (pdf) and cumulative distribution function (cdf) of the NXL distribution are given, respectevely, by…”

Section: The Poisson New X-lindley Distribution and Its Statistical P...mentioning

confidence: 99%

New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One

Irshad,

Aswathy,

Maya

et al. 2023

Count data arise in inference, modeling, prediction, anomaly detection, monitoring, resource allocation, evaluation, and performance measurement. This paper focuses on a one-parameter discrete distribution obtained by compounding the Poisson and new X-Lindley distributions. The probability-generating function, moments, skewness, kurtosis, and other properties are derived in the closed form. The maximum likelihood method, method of moments, least squares method, and weighted least squares method are used for parameter estimation. A simulation study is carried out. The proposed distribution is applied as the innovation in an INAR(1) process. The importance of the proposed model is confirmed through the analysis of two real datasets.