In many areas of applied sciences, the last step of a study often consists in analyzing in depth the collected data. Among all the kinds of data, the lifetime data are well-known to convey a great deal of information whose capture is necessary to identify one or more key phenomena. In this regards, numerous mathematical models have been proposed, including those based on lifetime distributions. In this paper, we introduce a new four-parameter lifetime distribution based on the type II Topp-Leone-G family and the power Lomax distribution. In comparison to the existing distributions, the new one is characterized by very flexible probability functions: increasing, decreasing, J, and reverse J shapes are observed for the probability density and hazard rate functions, giving first signs on the potential of adaptability of the related model. With this idea in mind, the new distribution is studied in detail, from both the theoretical and applied sides. After showing its main mathematical properties, the related model is investigated with estimation of the parameters by the maximum likelihood method. We applied it to two practical datasets, including the well-know aircraft windshield data. We show that the new model performs better than several modern adversary models, motivating its use in an applied setting.

Modern reliability engineering accelerated life tests (ALT) and partially accelerated life tests (PALT) are widely used to obtain the timely information on the reliability of objects, products, elements, and materials as well as to save time and cost. The ALTs or PALTs are useful in determining the failed manners of the items at routine conditions by using the information of the data generated from the experiment. PALT is the most sensible method to be used for estimating both ordinary and ALTs. In this research, constant stress PALT design for the Fréchet distribution with type-I censoring has been investigated due to a wide applicability of the Fréchet distribution in engineering problems especially in hydrology. The distribution parameters and acceleration factor are obtained by using the maximum likelihood method. Fisher's information matrix is used to develop the asymptotic confidence interval estimates of the model parameters. A simulation study is conducted to illustrate the statistical properties of the parameters and the confidence intervals by using the R software. The results indicated that the constant stress PALT plan works well. Moreover, a numerical example is given to exemplify the performance of the proposed methods.

The last years have revealed the importance of the inverse Lomax distribution in the understanding of lifetime heavy-tailed phenomena. However, the inverse Lomax modeling capabilities have certain limits that researchers aim to overcome. These limits include a certain stiffness in the modulation of the peak and tail properties of the related probability density function. In this paper, a solution is given by using the functionalities of the half logistic family. We introduce a new three-parameter extended inverse Lomax distribution called the half logistic inverse Lomax distribution. We highlight its superiority over the inverse Lomax distribution through various theoretical and practical approaches. The derived properties include the stochastic orders, quantiles, moments, incomplete moments, entropy (Rényi and q) and order statistics. Then, an emphasis is put on the corresponding parametric model. The parameters estimation is performed by six well-established methods. Numerical results are presented to compare the performance of the obtained estimates. Also, a simulation study on the estimation of the Rényi entropy is proposed. Finally, we consider three practical data sets, one containing environmental data, another dealing with engineering data and the last containing insurance data, to show how the practitioner can take advantage of the new half logistic inverse Lomax model.

Preceding studies have only been conducted with clear, determinate data, as the classical statistics approach is unable to accommodate ambiguity and uncertainty. As a generalization and alternative to classical statistics for such indeterminate or uncertain data, neutrosophic statistics is concerned with dealing such ambiguity in data. Making use of neutrosophic data, we propose a generalized class of estimators for the population mean under simple random sampling. Based on the numerical outcome it is presented that the suggested estimators achieved well in terms of minimum MSE. In order to more accurately represent the range of values throughout which our population parameter occurs, the results of these estimators are provided as intervals rather than a single value. We use simulation and interval data from the Islamabad Stock Exchange, focused on the UBL, to further investigate the efficiency of the suggested neutrosophic estimator. The numerical results confirm the suggested generalized neutrosophic estimators are superior to the existing methods. The mean square error (MSE) and percentage relative efficiency (PRE) performance measures demonstrate that the developed neutrosophic regression type estimator is always better than the conventional neutrosophic ratio estimator, neutrosophic product estimators, and the neutrosophic exponential ratio estimator. This paper addresses concerning how the neutrosophic regression estimator can make estimates more accurate when working with data that is unclear or uncertain and has a wide range of correlation between the study and the auxiliary variables that are being examined.

Point estimates have their limitations in survey sampling due to the fact that they provide just a single value for the parameter under study, which may vary between samples due to sampling errors. By producing interval estimates of the expected position of the parameter, the neutrosophic approach serves as a viable alternative in sampling theory. The neutrosophic approach optimizes the traditional strategy for effectively handling ambiguous data. To find the mean of the population using neutrosophic information we introduce a new family of estimators that incorporate additional information. Discovering the bias and mean square error is performed up to the first-order approximation. These estimators are ideal for data which is logical, confused, or ambiguous. This estimator is designed to make neutrosophic statistics (NS) in basic random sampling easier to understand. To better show the range of possible values for our population parameter, we show numerical findings for these estimators as intervals rather than single points. To further assess the efficiency of our proposed neutrosophic estimator, we utilize interval data and simulation derived from the Islamabad Stock Exchange (ISE).