Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm transformed-inverse (...) Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution. (shrink)

The problem of finding optimal sampling schemes has been resolved in two models. The novelty of this study lies in its cost efficiency, specifically, for the applied problems with expensive sampling process. In discussed models, we show that some observations counteract other ones in prediction mechanism. The autocovariance function of underlying process causes mentioned result. Our interesting result is that, although removing neutralizing observations convert sampling scheme to nonredundant case, it causes to worse prediction. A simulation study confirms this matter, (...) too. (shrink)

Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic- X family. The suggested NFLog- X family is obtained by applying the T- X method together with the exponential model having the PDF m (...) t = e − t. Based on the NFLog- X approach, a three parameters probability distribution, namely, a new flexible logarithmic-Weibull distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog- X family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog-Wei distribution. Comparisons are made between the analytical goodness-of-fit metrics of the suggested distribution. We made comparison with the alpha power transformed Weibull, exponentiated Weibull, Weibull, flexible reduced logarithmic-Weibull, and Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions. (shrink)

The extended reduced Kies distribution, which is an asymmetric flexible extension of the reduced Kies distribution, is the subject of this research. Some of its most basic mathematical properties are deduced from its formal definitions. We computed the ExRKD parameters using eight well-known methods. A full simulation analysis was done that allows the study of these estimators’ asymptotic behavior. The efficiency and applicability of the ExRKD are investigated via the modeling of COVID-19 and milk data sets, which demonstrates that the (...) ExRKD delivers a better match to the data sets when compared to competing models. (shrink)

The extended neoteric ranked set sampling plan proposed by Taconeli and Cabral has proven to outperform many one stages and two stages ranked set sampling plans when estimating the mean and the variance for different populations. Therefore, in this paper, the likelihood function based on ENRSS is proposed and used for estimation of the parameters of the inverted Nadarajah–Haghighi distribution. An extensive Monte Carlo simulation study is conducted to assess the performance of the proposed likelihood function, and the efficiency of (...) the estimated parameters based on ENRSS is compared with the well-known ranked set sampling plan and some of its modifications. These modifications include the extended ranked set sampling plan and the neoteric ranked set sampling plan. The results as foreseeable were very satisfactory and gave similar results to Taconeli and Cabral’s 2019 results. (shrink)