Correcting the error in getnetworkhashrateps

The discussion revolves around a statistical analysis concerning the estimation of network parameters in blockchain technology, particularly focusing on how to accurately calculate variances by applying the correct statistical distributions. The primary confusion addressed is the selection between Beta and Gamma (or Erlang) distributions for certain calculations and whether the Binomial or Poisson distribution should be used under specific conditions. This inquiry stems from an observed discrepancy in variance calculation when increasing the parameter (k) by 1 in a given formula. The concern is highlighted by a detailed example involving hypothetical hash rates and the selection of statistical models to estimate certain network characteristics.

The core of the argument lies in the observation that when one increases the set (S) by adding an element to it, thus forming (S'), and then recalculates the work (W) using a slightly higher hash rate (T), there seems to be a discrepancy in how the variance's denominator changes, suggesting a possible misapplication of the Beta distribution where perhaps the Gamma or Binomial distributions would be more appropriate. The discussion suggests that the Beta distribution's equation for work (W) becomes comparable to that of the Poisson's under constant difficulty, but with differing approaches to calculating variance, indicating a potential mismatch in the application of these statistical models.

This conversation further explores the necessity of adjusting the mathematical approach when counting events within a fixed amount of time versus counting time across a fixed number of events. It suggests that while the Poisson distribution is suited for scenarios with a fixed period, the Beta distribution may inaccurately describe situations where the goal is to count time across a fixed number of blocks. Instead, it proposes the use of the Binomial distribution in place of the Beta for time-fixed analyses and hints at employing the Gamma (or Erlang) distribution instead of the Poisson when the analysis looks back a fixed number of blocks.

The intricacies of these statistical tools and their application to blockchain analysis underscore the complexity of accurately modeling and predicting network behavior. The discussion implies a deep understanding of both blockchain mechanics and statistical theory, emphasizing the critical nature of choosing the correct model for variance calculation to ensure accurate representations of network dynamics. This exploration not only highlights the challenges faced in such analytical exercises but also calls for a more nuanced approach to applying statistical distributions in the context of blockchain and cryptocurrency analysis.