This study examines the use of Filtered Historical Simulation (FHS) to estimate tail risk in cryptocurrency markets for the optimization of robustness in this area under model misspecification. An ARMA-GARCH model is employed on the daily returns on Binance Coin and Litecoin in order to compare...

Financial time-series data often exhibit statistically significant skewness and heavy tails, and numerous flexible distributions have been proposed to model them. In the context of the Log-linear Realized GARCH model with Skew-t (ST) distributions, our objective is to explore how the choice of...

The Pareto distribution has been widely used to model income distribution and inequality. The tail index and the Gini index are typically computed by iteration using Maximum Likelihood and are usually interpreted in terms of the Lorenz curve. We derive an alternative method by considering a...

This paper reviews earlier applications of Benford's Law to the COVID-19 data in the United States that claimed these data's non-conformity with Benford's Law, and uses later and more granular data to demonstrate that this was likely due to the earlier data being unsuitable for such...

Area-biased distributions are special cases of size-biased distributions. We have used the idea of area-biased distributions in this paper to propose a generalisation of a one-parameter linear exponential distribution. The concept is called the area-biased one-parameter linear exponential...

This paper explores classical and Bayesian approaches to the estimation of unknown parameters and reliability functions for the power Rayleigh distribution. The maximum likelihood estimator (MLE) method is considered in classical estimation. The Bayesian estimation, on the other hand uses...

In statistical analysis, evaluating the normality of large datasets is crucial for validating parametric tests, particularly in areas such as Global Navigation Satellite System (GNSS) measurements, where data often exhibit non-normal characteristics resulting from their variability and errors....

Modeling loss data is a crucial aspect of actuarial science. In the insurance industry, small claims occur frequently, while large claims are rare. Traditional heavy-tail distributions, such as Weibull, Log-Normal, and Inverse Gaussian distributions, are not suitable for describing insurance...

The maximum drawdown of a stochastic process is the largest peak-to-trough decline observed over a given horizon [0, T]. Using arguments from extreme value theory, we derive the limiting distribution of the maximum drawdown for a Brownian motion with positive drift as T → ∞. We show that,...

In this study, we propose a Gram-Charlier expansion approach to investigate the impact of skewness and kurtosis on production and hedging decisions. Consistent with the existing literature, we find that skewness and kurtosis do not affect decisions regarding optimal production; however, they...

This paper studies asymmetry in economic activity in a multisector model with shocks to productivity and labor wedges. Complementarity across inputs - creating nonlinear intersectoral interactions - creates negative skewness. The analysis generates additional predictions: skewness is smaller at...

The dynamic weighted cumulative residual (DWCR) entropy is regarded as an additional measure of uncertainty related to the residual lifetime function in several disciplines, including survival analysis and reliability. This article presents the DWCR formula based on Havarda and Charvat. This...

Maximum likelihood estimation (MLE) in infinite mixture distributions often lacks closed-form solutions, requiring numerical methods such as the Newton-Raphson algorithm. Selecting appropriate initial values is a critical challenge in these procedures. This study introduces a bootstrap-based...

This paper studies how a forward-looking decision maker experiments on unknown alternatives of correlated utilities. The utilities are modeled by a Brownian motion such that similar alternatives yield similar utilities. Experimentation trades off between the continuation value of exploration and...

We investigate the conditional tail behaviour of asset price changes at high (10-second) frequencies using a new dynamic model for integer-valued tickdata. The model has fat tails, scale dynamics, and allows for possible over- or under-representation of zero price changes. The model can be...

This study examines the impact that fat-tailed distributions of the spread residuals have on the optimal orders for pairs trading of stocks and cryptocurrencies. Using daily data from selected pairs, the spread dynamics has been modeled through a mean-reverting Ornstein-Uhlenbeck process and...