179 Results Found

In this paper, we introduce a new probability distribution defined on the unit interval $(0,1)$, called the unit extended exponential (UEE) distribution. The proposed model is obtained through a transformation of a random variable following the extende...

The significance of count data modeling and its applications to real-world phenomena have been highlighted in several research studies. The present study focuses on a two-parameter discrete distribution that can be obtained by compounding the Poisson...

In this paper, we provide explicit expressions as well as recurrence relations for the single and product moments of generalized order statistics from the log-extended exponential–geometric distribution. These relations are utilized to discuss...

Bounded observations occur in a variety of applied scenarios such as reliability probabilities, degradation measures, rates, and other functions defined on the unit interval for which flexible distributional and hazard-rate behavior are desired. This...

In this paper, the Extended Half-Power Exponential (EHPE) distribution is built on the basis of the Power Exponential model. The properties of the EHPE model are discussed: the cumulative distribution function, the hazard function, moments, and the s...

Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create...

In this paper, the parameters of the extended odd Weibull exponential distribution are estimated under progressive type-II censoring scheme with random removal. The model parameters are estimated using the maximum product spacing and maximum likeliho...

The classical Cox model is the most popular procedure for studying right-censored data in survival analysis. However, it is based on the fundamental assumption of proportional hazards (PH). Modified Cox models, stratified and extended, have been wide...

In this article, four new families named as Weibull extended exponentiated-X (WEE-X), Lomax extended exponentiated-X (LEE-X), Logistic extended exponentiated-X (LGCEE-X), and Burr III extended exponentiated-X (BIIIEE-X) with their quantile functions...

Traditional DEA models can neither effectively handle fuzzy random variables nor achieve a complete ranking of decision-making units (DMUs). Based on the conventional fuzzy stochastic DEA model, this study introduces an exponential distribution exten...

Here, we propose a new generalized exponential extended exponentiated (NGE3) family of distributions. Some statistical properties of proposed family are gained. The most extreme probability method, maximum likelihood (ML), is utilized for parameter e...

Statistical Process Control (SPC) plays a crucial role in monitoring and improving manufacturing processes to ensure product quality. Control charts using exponentially weighted moving averages (EWMA) and their extensions, including Extended EWMA (EE...

In this paper, we reparameterized the extended exponential model based on the mean in order to include covariates and facilitate the interpretation of the coefficients. The model is compared with common models defined in the positive line also repara...

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for p...

Log-concavity and log-convexity play a key role in various scientific fields, especially in those where the distinction between exponential and non-exponential distributions is necessary for inferential purposes. In the present study, we introduce a...

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following co...

This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers...

Environmental and financial datasets often display complex distributional characteristics, including heavy tails, high skewness and the presence of extreme observations. Traditional probability models such as the exponential, gamma or log-normal dist...

The classical exponential (Exp) distribution may have limited capability in describing asymmetric lifetime data and observations with different tail characteristics. In this paper, a new extended exponential model, called the Mixed Exponential–...

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are...

In this paper, we develop the new extended Kumaraswamy generated (NEKwG) family of distributions. It aims to improve the modeling capability of the standard Kumaraswamy family by using a one-parameter exponential-logarithmic transformation. Mathemati...

In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of p...

In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd We...

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen...

This paper proposes a novel statistical test for evaluating exponentiality against the recently introduced EBUCL (Exponential Better than Used in Convex Laplace transform order) class of life distributions. The EBUCL class generalizes classical aging...

From an information geometric perspective, this study considers a natural foliation of dualistic structures associated with escort distributions of exponential families. We propose an extended divergence on this foliation by continuous-type escort di...

The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accom...

This paper elucidates the prerequisites for maximum likelihood estimation (MLE) of parameters within the exponential and scale parameter families. Estimation of these parameters is predicated on data derived from censored samples and seeks to adhere...

We propose the Bivariate Poisson–X–Exponential Distribution (BPXED), a flexible bivariate count model obtained by compounding Poisson variables with a shared X–Exponential latent mixing distribution. The model extends the Poisson&nd...

In this article, we introduce a new extended cosine family of distributions. Some important mathematical and statistical properties are studied, including asymptotic results, a quantile function, series representation of the cumulative distribution a...

Anomalous deviations from the Beer-Lambert law have been observed for a long time in a wide range of application. Despite all the attempts, a reliable and accepted model has not been provided so far. In addition, in some cases the attenuation of radi...

In the paper, an overview is presented of the results on the convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson random sums, including the case where the mixing law is itself a mixed...

A control chart is a crucial statistical process control (SPC) instrument for identifying method variances that may undermine product efficacy. The combined control chart has been utilized to enhance recognition capability. When testing a methodology...

A fully parametric accelerated failure time (AFT) model with a flexible, novel modified exponential Weibull baseline distribution called the extended exponential Weibull accelerated failure time (ExEW-AFT) model is proposed. The model is presented us...

In this paper, we study a new flexible three-parameter exponential distribution called the extended odd Weibull exponential distribution, which can have constant, decreasing, increasing, bathtub, upside-down bathtub and reversed-J shaped hazard rates...

The fracture of the Mg/Mg₁₇Al₁₂ interface was investigated by molecular dynamics simulations. The interface crack extends in a brittle manner without noticeable plasticity. The distributions of normal stress and separation along the interface were ex...

In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more...

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continu...

In this paper, we study the problem of solving Seal’s type partial integro-differential equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep neural network (DNN) method is proposed to calculate finite-time surviva...

The Clopper–Pearson method of constructing a confidence interval for the probability of success in a binary population that follows a Bernoulli distribution is well known. This paper pedagogically justifies the Clopper–Pearson method and...

A new three-parameter survival model is proposed using the Kavya–Manoharan (KM) transformation family and the exponentiated Weibull (EW) distribution. The shapes of the pdf for the new model can be asymmetric and symmetric shapes, such as unimo...

Matrix-variate Gaussian-type or Wishart-type distributions in the real domain are widely used in the literature. When the exponential trace has an arbitrary power and when the factors involving a determinant and a trace enter into the model or a matr...

The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ide...

The univariate Topp–Leone distribution introduced by with closed forms of the cumulative distribution function, i.e., [0, 1], was extended to an unbounded limit called the log-Topp–Leone distribution, where the shapes of the hazard functi...

Deriving loss distribution from insurance data is a challenging task, as loss distribution is strongly skewed with heavy tails with some levels of outliers. This paper extends the weighted exponential (WE) family to the contaminated WE (CWE) family,...

In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important appl...

Practitioners often face the situation of comparing any set of k distributions, which may follow neither normality nor equality of variances. We propose a semiparametric model to compare those distributions using an exponential tilt method. This exte...

In this article, we propose a new transmuted modified power-generalized family of distributions constructed from the transmuted-generated and modified power-generated families. The proposed approach is flexible and provides a tradeoff between the two...

This paper extends the k-out-of-n:G reliability system to a multi-server queue. We study a multi-server reliability-queuing model with the N-policy of repair. The queuing system considered here has n servers, each of which has identically and exponen...

A new two-parameter extended exponential lifetime distribution with an increasing failure rate called the Poisson–exponential (PE) model was explored. In the reliability experiments, an adaptive progressively Type-II hybrid censoring strategy i...