Allowance for skewness in maximum-likelihood estimation with application to the location-scale model

The use of maximum-likelihood estimation as discussed by Sprott and Viveros (1984) is extended to include the log F distribution to accommodate skewness. The role played by linear pivotals in relation to likelihood and efficiency is discussed. Normal, t, and log F likelihoods are defined and used to generate possible normal, t, and log F linear pivotal quantities. The results are applied to the location-scale family, where exact results are available to assess the numerical accuracy of the proposed procedure. Refinements using saddlepoint approximations are obtained.