Forecasting the Climate Change through the Distributions of Solar Radiation and Maximum Temperature

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 ((, )) 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 (, ) 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 () and () with minimal error

Algorithms of Solar Energy Prediction Combined with Percentile Root Estimation of Three-Parameters Distributions

We propose three algorithms to the problem of solar energy prediction and Percentile Root Estimation (PRE) of three- parameters distributions. The first algorithm named Algorithm of Change Rate Matrix (ACRM), Our approach is based on creating a matrix of solar energy change rates for each month separately during successive years. ACRM is characterized by not relying on the transition matrix or Markov model. The second algorithm named Algorithm of Converting Dataset to Markov model (ACDM) depends on the transition states of the solar energy and Markov model for a month during successive years. The results were compared with the actual values to validate the algorithms ACRM and ACDM. We demonstrate the ability of the mentioned algorithms to perform on the other dataset in various applications. The third algorithm PRE applied on the distributions Lognormal, Fatigue lifetime, Erlang, Fre ́chet and Pert which it was validated using Goodness-fit-tests, Anderson-Darling test. We analyzed the influence of PRE algorithm, as a result it is more accurate and easier in coding than the maximum likelihood estimation method

Alpha-Power of the Power Ailamujia Distribution: Properties and Applications

This paper deals with a novel distribution defined as Alpha Power of the Power Ailamujia distribution (APPA). Using the power transformation technique, which incorporates an extra parameter of the distribution, the proposed distribution is obtained. The quantile function, moments, moment generating function, characteristics function, mode, median, order statistics, Shannons entropy, survival measures and other properties have been studied for the newly developed distribution. The behavior of probability density function (pdf), cumulative distribution function (cdf), survival function and hazard rate function are illustrated through various plots. The method of maximum likelihood estimation has been used to estimate the parameters of this distribution. Finally, the APPA distribution is more suitable than other competing distributions, according to four real data, including two COVID-19 data in two countries that were taken into consideration to assess the utility of the established distribution