Cryptocurrency is a digital currency and also exists in the form of coins. It has turned out as a leading method for peer-to-peer online cash systems. Due to the importance and increasing influence of Bitcoin on business and other related sectors, it is very crucial to model or predict its behavior. Therefore, in recent, numerous researchers have attempted to understand and model the behaviors of cryptocurrency exchange rates. In the practice of actuarial and financial studies, heavy-tailed distributions play a fruitful role in modeling and describing the log returns of financial phenomena. In this paper, we propose a new family of distributions that possess heavy-tailed characteristics. Based on the proposed approach, a modified version of the logistic distribution, namely, a new modified exponential-logistic distribution is introduced. To illustrate the new modified exponential-logistic model, two financial data sets are analyzed. The first data set represents the log-returns of the Bitcoin exchange rates. Whereas, the second data set represents the log-returns of the Ethereum exchange rates. Furthermore, to forecast the high volatile behavior of the same datasets, we apply dual machine learning algorithms, namely Artificial neural network and support vector regression. The effectiveness of these models is evaluated against self exciting threshold autoregressive model.

In this article, estimation of the parameters as well as some lifetime parameters such as reliability and hazard rate functions for the Dagum distribution based on record statistics is obtained. Both Bayesian and non-Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. Moreover, approximate confidence intervals for the parameters based on the asymptotic distribution of the maximum likelihood estimators are constructed. Besides, to construct the variances of the reliability and hazard rate functions the delta method is implemented. The Lindley's approximation and Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under both symmetric and asymmetric loss functions. Also, the corresponding highest posterior density credible intervals are constructed. A simulation study is utilized to assay and evaluate the performance of the proposed inferential approaches. Finally, a real data set of COVID-19 mortality rate is analyzed to illustrate the proposed methods of estimation.