Results on Enhanced Continuous Random Variable’s Probability Distribution Using a Different Exponential Function for the Normal Probability Distribution (Contemporary Mathematics, 2025)
In the history of probability and statistics, general normal probability has played an important role. I utilize a different exponential function to create a new continuous probability density function akin to the Laplace Gauss distribution function. Finding an alternate probability distribution is required so that the probability can be determined without referring to the table data. I noticed that the findings are pretty comparable to the normal probability distribution values. I checked the new results against a few standard cases. The advantage of this exponential function is that we can calculate the probability of a z value with more than two decimals, whereas with a normal distribution, we can only use z  values with two decimals.
Keywords: random variable; normal probability distribution; error function; hyperbolic secant function; cumulative probability distribution