Refined Inference on the Scale Parameter of the Generalized Logistic Distribution Based on Adjusted Profile Likelihood Functions

We consider inference based on the profile likelihood function for scale parameter of generalized logistic distribution. This distribution is a generalization distribution, symmetric like normal and it has several applications in various fields. The allows possible left or right skewness, which makes more flexible modeling purposes. Inference procedures do not perform very well when sample size small, therefore, we derived adjustments to using results from higher-order theory. obtained an adjustment empirical covariances certain scores function. Another ancillary statistics. performance investigated point estimation bias mean squared error criteria. Using extensive simulation study, found are successful reducing maximum estimator most situations. Moreover, studied ratio test its criterion attainment nominal sizes. that, sizes that highly inflated. Therefore, will be invalid such Simulation show adjusted versions produce tests attain even small samples. also applies confidence intervals these tests. In conclusion, both have significantly better than unadjusted recommended, especially particular, statistics appears best overall all situations considered. applied methods this paper real data Carbon fibers.