Exponential-gamma-Rayleigh distribution and its applications

probability distribution help researcher and practitioners understand and model complex behaviour of rainfall data, ultimately behaviour of rainfall data and decision making in field of hydrology, water resource management and climate change impact assessment which intensify for specific duration simulation event and generate synthetic rainfall data and also optimize water resource management by modelling the probability of future rainfall scenarios Understanding and interpreting data behaviour more scientifically is an essential stage in every field of life. Statistical methods are used in applied in fields of hydrological, and mesosphere and lower thermosphere weather observations. Several researchers have generated new adaptable distributions from existing distributions using various modification techniques to increase their flexibility in rainfall modelling data. These adaptable distributions are created by adding extra parameters to the baseline distribution with generators or combining two distributions (Ali, et al., 2021). These modified distributions can model data sets efficiently and in most case, provide the best fit to data sets when applied because they have more parameters and are more adaptable than their baseline distributions. Data on the thirty observations for March rainfall in Minneapolis/St Paul (in inches), the data set has been used by Isa, et al., (2022), data sets obtained from Lee and Wang, (2003), and , the data set obtained from Fatima and Ahmad, (2017), which represents the 72 exceedances of flood maxima (in m3/s) of the Wheaton River near Carcoss in Yukon Territory, Canada, from 1958 to 1984 (rounded to one decimal point). The newly developed probability distributions robustness and versatility are evaluated by comparing them to other related existing probability distributions, such as the Exponential, Gamma, and Rayleigh distributions. Also, the Exponential-Gamma distribution developed by Ogunwale, et al., (2019), using goodness of fit measurements The Python 3.10.10 software package was used to analyse the data. The Akaike information criterion (AIC), Bayesian information criterion (BIC), and log-likelihood function (l) are the goodness of fit measures discussed. The probability distribution with the lowest Akaike information criterion (AIC), Bayesian information criterion (BIC), or highest log-likelihood function (l) value will be used to determine the best-suited model.