In this paper, based on a doubly generalized Type II censored sample, the maximum likelihood estimators (MLEs), the approximate MLE and the Bayes estimator for the entropy of the Rayleigh distribution are derived. We compare the entropy estimators' root mean squared error (RMSE), bias and Kullback-Leibler divergence values. The simulation procedure is repeated 10,000 times for the sample size n = 10, 20, 40 and 100 and various doubly generalized Type II hybrid censoring schemes. Finally, a real data set has been analyzed for illustrative purposes.

Roads are notable and responsible for the loss of biodiversity and disruption of wildlife habitats connectivity. Wildlife crossing structures (WCS) help wildlife move between habitats by connecting fragmented habitats. Their effectiveness is affected by various factors. Here, to identify methods for improving the effectiveness of wildlife crossing structures, we controlled the effect of intrinsic factors, such as size, that are difficult to improve in an already installed area, and then, evaluated the differences in extrinsic factors using 12 landscape characteristics. Our results show that 18 wildlife crossing structures were selected with propensity-score (PS) matching method. The surrounding landscape characteristics differed between high-effectiveness wildlife crossing structures and low-effectiveness wildlife crossing structures. Particularly, there was a significant difference between the ‘statutory protected area’ and the ‘edge’ index of the morphological spatial pattern analysis among the landscape characteristic variables derived within 1 km2 of wildlife crossing structures. We empirically demonstrate that characteristics around highly effective WCS, statutory protected areas are widely distributed, and the ratio of edge of MSPA is low (within 1 km2). Therefore, an important outcome of our research is the demonstration that management of WCS itself is important, but conservation of surrounding habitats and landscape management plans are also significant.

It is known that the lifetimes of items may not be recorded exactly. In addition, it is known that more than one risk factor (RisF) may be present at the same time. In this paper, we discuss exact likelihood inference for competing risk model (CoRiM) with generalized adaptive progressive hybrid censored exponential data. We derive the conditional moment generating function (ConMGF) of the maximum likelihood estimators of scale parameters of exponential distribution (ExpD) and the resulting lower confidence bound under generalized adaptive progressive hybrid censoring scheme (GeAdPHCS). From the example data, it can be seen that the PDF of MLE is almost symmetrical.

In many situations of survival and reliability test, the withdrawal of units from the test is pre-planned in order to to free up testing facilities for other tests, or to save cost and time. It is known that several risk factors (RiFs) compete for the immediate failure cause of items. In this paper, we derive an inference for a competing risks model (CompRiM) with a generalized type II progressive hybrid censoring scheme (GeTy2PrHCS). We derive the conditional moment generating functions (CondMgfs), distributions and confidence interval (ConfI) of the scale parameters of exponential distribution (ExDist) under GeTy2PrHCS with CompRiM. A real data set is analysed to illustrate the validity of the method developed here. From the data, it can be seen that the conditional PDFs of MLEs is almost symmetrical.

The inverse Weibull distribution (IWD) can be applied to a various situations, including applications in reliability and medicine. In a reliability and medicine test, it is generally known that the results of test units may not be recorded. Recently, the generalized adaptive progressive hybrid censoring (GAPHC) scheme was introduced. In this paper, therefore, we consider the classical estimators (maximum likelihood estimator (MLE) and maximum product spacings estimator (MPSE)) and Bayes estimators (BayEsts) of the uncertainty measure of the IWD under GAPHC scheme. We derive the BayEsts of the uncertainty measure based on flexible (symmetrical and asymmetrical) priors. Additionally, we derive the Bayes estimators using the Tierney and Kadane approximation (TiKa) and importance sampling methods. In particular, the importance sampling method is used to obtain the credible interval for the uncertainty measure of the IWD under the GAPHC scheme. To compare the proposed estimators (classical and BayEsts), the Monte Carlo simulation method is conducted. Finally, the real dataset based on GAPHC scheme is analyzed.

Recently, the generalized type I progressive hybrid censoring scheme (GenT1PrHyCS) and generalized type II progressive hybrid censoring scheme (GenT2PrHyCS) have become quite popular in reliability studies. These two type censoring schemes are very complex due to the large number of parameters used to specify the censoring procedure. Therefore, in this paper, we consider a more general and more complex new censoring scheme. Also, we consider the exponential distribution(ExpD) and derive an expression for the density function of the MLE. We prove the exact distribution of the maximum likelihood estimator (MLE) and conditional moment generating function (CondMGF) of the MLE for the mean of the ExpD under a new censoring scheme. We then derive the exact confidence intervals (ConfItv) for the mean of the ExpD under a new censoring scheme. Finally, we present an example to explain the methods of inference derived for this paper. From the example data, it can be seen that PDF of MLE for ExpD under new censoring scheme is almost symmetrical.