In the paper, we looked at the problem of employing several non-Bayesian estimation approaches to estimate the parameters of the Type-I half-logistic skew-t (TIHLST) model. The maximum likelihood, least squares, weighted least squares, Anderson-Darling, maximum product of spacing, and Cramer-von Mises are the six methods for TIHLST parameter estimation that we examined. The Monte Carlo simulations were used to assess the TIHLST parameter estimations’ finite sample performance. The partial and overall ranks of the estimating techniques for every combination of parameters were used to determine the ordering performance of the six criteria. Based on the overall ranks, the results indicate that the criteria performance is ranked from best to worst using the following estimators: maximum likelihood, weighted least squares, maximum product of spacing, least squares, and Cramer-von Mises for all parameter combinations. Based on an overall rank of 34, we infer that the maximum-likelihood criterion fared better than all other criteria. For the TIHLST model, we thereby affirm the supremacy of the maximum likelihood criterion with an overall rank of 34 and the Anderson-Darling criterion with an overall rank of 57.5.