Journal of Statistics Applications & Probability

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The climate change crisis is negatively affecting the world and is the focus of many researchers attention for its life-threatening economic and climate impact on Earth. Therefore, this study aims to estimate the joint distribution function (EFXY) of both daily solar radiation (S) and daily maximum temperature (T) along with the Markov property. In this study, three-parameter distributions have been utilized with S and T, which are generalized extreme value (GEV) and Weibull (W-3P), respectively. Each of these parameters and the joint distribution function (𝐹(𝑋, π‘Œ)) have been estimated. Four real data of S and T in Queensland, Australia during two consecutive years are applied. The method of maximum likelihood estimation (MLE) is applied on the proposed distributions of S and T to estimate their parameters, which was validated using Goodness-of-Fit tests. In addition, the logarithmic (LFXY) model and the multi-regression model (MFXY) for 𝐹(𝑋, π‘Œ) are obtained. The results have been compared and the EFXY and LFXY are found to be non-equivalently, while the EFXY and MFXY are equivalent and homogeneous, confirming the validity of the joint distribution function estimate with the least error. Thus, the climate change probabilities are more accurately predictable by knowing both X and Y or by knowing both 𝐹(𝑋) and 𝐹(π‘Œ) with minimal error.

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