Truncated models are imperative to efficiently analyze the finite data that we observe in almost all the real life situations. In this paper, a new truncated distribution having four parameters named Weibull-Truncated Exponential Distribution (W-TEXPD) is developed. The proposed model can be used as an alternative to the Exponential, standard Weibull and shifted Gamma-Weibull and three parameter Weibull distributions. The statistical characteristics including cumulative distribution function, hazard function, cumulative hazard function, central moments, skewness, kurtosis, percentile and entropy of the proposed model are derived. The maximum likelihood estimation method is employed to evaluate the unknown parameters of the W-TEXPD. A simulation study is also carried out to assess the performance of the model parameters. The proposed probability distribution is fitted on five data sets from different fields to demonstrate its vast application. A comparison of the proposed model with some extant models is given to justify the performance of the W-TEXPD.

Gul and Mohsin 2021 developed a new modified form of renowned “Half logistic” distribution introduced by Balakrishnan (1991) and named it half logistic-truncated exponential distribution (HL-TEXPD). Some mathematical characteristics are studied, including hazard function, P^th percentile, moment generating function and Shannon entropy. Simulation study is performed to examine the behaviour of parameter estimates. The proposed model is fitted on three real data sets to check its efficacy. Additionally, TTT (total time on test) plot is drawn to study the failure rate of the three data sets. The results verdict that HL-TEXPD can be efficiently utilized in the field of engineering and medical sciences based on the data sets under study contrary to the classical and baseline models.

A new distribution named half logistic-truncated exponential distribution having location and scale parameters is developed. The recurrence relations are established for the single moments and product moments of order statistics for various values of scale parameter theta. These recurrence relations are used to calculate the first k moments of all order statistics in a simple and efficient manner and to tabulate means, variances and covariances in samples of size n = 1(1)10.

To meet the desired standard, it is important to monitor and analyze different engineering processes to obtain the desired output. The bivariate distributions have received a significant amount of attention in recent years due to their ability to describe randomness of natural as well as artificial mechanisms. In this article, a bivariate model is constructed by compounding two independent asymmetric univariate distributions and by using the nesting approach to study the effect of each component on reliability for better understanding. Furthermore, the Bayes analysis of system availability is studied by considering prior parametric variations in the failure time and repair time distributions. Basic statistical characteristics of marginal distribution like mean median and quantile function are discussed. We used inverse Gamma prior to study its frequentist properties by conducting a Monte Carlo Markov Chain (MCMC) sampling scheme.

Traditionally, infinite models have been fitted on finite datasets which extrapolate the data, resulting in inadequate model fitting and predictions. To overcome this problem, we develop a new family of truncated distributions by introducing a new generator. In this article, a truncated random variable X_tr “the transformer or input” is exerted to transform another random variable T “transformed or generator,” which yields a new T − X_tr family of distributions. Several characteristics of T − X_tr family of distributions are provided which are equally useful in engineering and biological sciences. For application purposes, a type‐2 Gumbel‐truncated exponential distribution is generated by using the proposed method along with its statistical properties. The efficacy of the new model is demonstrated by applying it to echophysiology and comparing the resulting outputs with those from the baseline models. Relevance of the Work. Indeed, the probability models have infinite domains but they are applied on the finite real datasets which may lead to exaggerated inferences and predictions. This problem can be solved by developing models that have finite domains. We propose finite models to analyze the finite data proficiently, provide reliable inferences, and save time.