Kavya-Manoharan Dinesh-Umesh-Sanjay (KM-DUS) Family of Distributions: Sub-model, Properties, Inference, Simulation and Applications

In this study, we construct a family of distributions that does not include additional parameter to any baseline distribution. This new family is a composition of two families of distributions, that is, the Kavya-Manoharan (KM) family and the Dinesh-Umesh-Sanjay (DUS) family and it is named the Kavya-Manoharan Dinesh-Umesh-Sanjay (KM-DUS) family. Further, an innovative two-parameter lifetime distribution being the KM-DUS Rayleigh-inverted Weibull (KM-DUS-RIW) distribution was proposed. In this new distribution, the Rayleigh-Inverted Weibull (RIW) was used as the baseline distribution. The new distribution is an improvement of the RIW in that it guarantees more flexibility and tractability with no increase in parameters hence offering a parsimonious but powerful tool for modeling reliability and survival data. The primary statistical characteristics of this KM-DUS-RIW distribution such as its probability density function, cumulative distribution function, quantile function, moments, and order statistic, have been derived and discussed in great detail. The methods named Maximum likelihood (ML), Least Squares (LS), Weighted Least Squares (WLS), Maximum Product Spacing (MPS), Cramér-von Mises (CVM), Anderson-Darling (AD), Right-Tailed Anderson-Darling (RTAD), Percentile (PERC) as well as Bayesian methods with different loss functions such as Squared Error, LINEX, and General Entropy are utilized for estimating the model parameters were explored. Of these, MPS consistently yields the most efficient estimates across various sample sizes. The practicality of the proposed distribution is exemplified by using real entomological data with adult progeny counts of Stegobium paniceum L. under choice and non-choice tests as application cases. Besides, the model is compared using the log-likelihood, AIC, BIC, HQIC, and several goodness-of-fit statistics, which show the KM-DUS-RIW model fits better than the competing available models. These findings attest to the KM-DUS-RIW distribution being a promising potential alternative to modeling complex lifetime data.