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 (NFLog‐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 (NFLog‐Wei) 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 (i) alpha power transformed Weibull, (ii) exponentiated Weibull, (iii) Weibull, (iv) flexible reduced logarithmic‐Weibull, and (v) Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions.

Bayesian networks are now widespread for modelling uncertain knowledge. They graph probabilistic relationships, which are quantified using conditional probability tables (CPTs). When empirical data are unavailable, experts may specify CPTs. Here we propose novel methodology for quantifying CPTs: a Bayesian statistical approach to both elicitation and encoding of expert-specified probabilities, in a way that acknowledges their uncertainty. We illustrate this new approach using a case study describing habitat most at risk from feral pigs. For complicated CPTs, it is difficult to elicit all scenarios (CPT entries). Like the CPT Calculator software program, we ask about a few scenarios (e.g. under a one-factor-at-a-time design) to reduce the experts' workload. Unlike CPT Calculator, we adopt a global rather than local regression to ‘fill out’ CPT entries. Unlike other methods for scenario-based elicitation for regression, we capture uncertainty about each probability in a sequence that explicitly controls biases and enhances interpretation. Furthermore, to utilize all elicited information, we introduce Bayesian rather than Classical generalised linear modelling (GLM). For large CPTs (e.g. >3 levels per parent) we show Bayesian GLM supports richer inference, particularly on interactions, even with few scenarios, providing more information regarding accuracy of encoding.

A long testing period is usually required for the life testing of high-reliability products or materials. It is possible to shorten the testing process by using ALTs (accelerated life tests). Due to the fact that ALTs test products in harsher settings than are typical use conditions, the life expectancy of the objects they evaluate is reduced. Censored data in which the specific failure timings of all units assigned to test are not known, or all units assigned to test have not failed, may arise in ALTs for a variety of reasons, including operational failure, device malfunction, expense, and time restrictions. In this paper, we have considered the step stress partially accelerated life test (SSPALT) under two different censoring schemes, namely the type-I progressive hybrid censoring scheme (type-I PHCS) and the type-II progressive censorship scheme (type-II PCS). The failure times of the items are assumed to follow NH distribution, while the tampered random variable (TRV) model is used to explain the effect of stress change. In order to obtain the estimates of the unknown parameters, the maximum likelihood estimation (MLE) approach is adopted. Furthermore, based on the asymptotic theory of MLEs, the approximate confidence intervals (ACIs) are also constructed. The point estimates under two censoring schemes are compared in terms of root mean squared errors (RMSEs) and relative absolute biases (RABs), while ACIs are compared in terms of their lengths and coverage probabilities (CPs). The performance of the estimators has been evaluated and compared under two censoring schemes with various sample sizes through a simulation study. Simulation results show that estimates with type-I PHCS outperform estimates with type-II PCS in terms of RMSEs, RABs, lengths, and CPs. Finally, a real-world numerical example of insulating fluid failure times is presented to show how the approaches will work in reality.