The sin extension of the exponential (SExEx) or sin Nadarajah-Haghighi (SNH) distribution, a new extension of the exponential distribution with two parameters, is introduced and studied in this paper. For the SNH distribution, the hazard, survival functions and some sumarized data are explored. Methods for estimating the SNH distribution parameters using maximum likelihood estimation (MLE) and maximum product spacing (MPS) are explored. To compare various estimating techniques, a numerical analysis using Monte-Carlo simulation and real data analysis is carried out. Environmental data show how the new model is superior to some well-known distributions. In comparison to several well-known distributions, the SNH model can give better matches.

Generating new statistical models is one of the most commonly used methods to represent real-life occurrences. Sometimes, with a known distribution, it may not be possible to represent a scenario, so we may consider generalization to incorporate more variance in the data. In this article, we offer a modified cubic transmuted-G family of distributions to enrich the members of the second-order transmuted distributions. By utilizing this modified class of distributions, we build a new distribution entitled the modified cubic transmuted Rayleigh distribution, along with its distributional features, estimate, associated inference, and real-life applications.

Probability distribution has proven its usefulness in almost every discipline of human endeavor. For this, the zero-truncated Poisson gamma (ZTP-G) model is widely recognized in probability theory and extensively used in various applied fields, specifically in survival, hydrology, insurance, and energy theory. The characterization of the zero-truncated Poisson sum of independent and identically distributed gamma random variables is proposed in this paper by applying the Laplace-Stieltjes transform technique. Further, the properties of continuity and quadratic form of the characteristic function are applied for definite positive properties from the ZTP-G model.

In the real world, many applications require enhanced variants of well-known distributions. The new distributions are generally more adaptable for simulating real-world data with high skewness and kurtosis. Choosing the best statistical distribution for modeling data is very important and demanding. In this paper, we provide a new fl exible model for modeling lifetime data that is achieved by adding a component to baseline distributions. The new model has three parameters, known as the exponential T-X Gompertz distribution. Its probability density function could be skewed and unimodal. Reliability, hazard rate, quantile, and the moment generating function are just a few of the distributional properties that can be inferred from the suggested model. To estimate the unknown parameters, maximum likelihood estimation is utilized. In addition, Monte Carlo simulation experiments are performed to evaluate the performance of the maximum likelihood estimators. Finally, two real-world data sets are shown to evaluate the proposed model’s potential with that of various existing models.