ALPHA LOGARITHM TRANSFORMED SEMI LOGISTIC DISTRIBUTION USING MAXIMUM LIKELIHOOD ESTIMATION METHOD

Abstract

In this article, we review the maximum likelihood method for estimating the parameters of a fitted model
and show that this method generally provides the asymptotically best estimate with the smallest mean
Error. Therefore, maximum likelihood estimation is sufficient for most applications in data science. The
Fisher data matrix describes the orthogonality of parameters in a probabilistic model and always results
from the highest possible estimate. Parameters associated with the model were estimated using the
Maximum Likelihood Estimation (MLE) method. The maximum likelihood estimation method in a risk
function is used to estimate the parameters of the alpha log-transformed semi-logistic distribution to
determine the best method. Since the inverse of the Fisher data matrix provides the variance matrix of the
prediction error, orthogonalizing the parameters ensures that the parameters are distributed independently
of each other. Finally, the extended model was applied to real data and results showing the performance
of ALTSL classification compared to other classification methods are presented. We present the MLE of
the unknowns in this distribution using Newton-Raphson. We also calculate the Average Estimation
(AE), Variance (VAR), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Relative Absolute
Bias (RAB) and Relative Efficiency (RE) for both the parameters under sample based on 10000
simulations to assess the performance of the estimators. Also, we derive the asymptotic confidence
bounds for unknown parameters.