  In this paper we investigate the performance of a variety of estimation
techniques for the scale and shape parameter of the Lomax distribution. These
methods include traditional methods such as the maximum likelihood estimator
and the method of moments estimator. A version of the maximum likelihood
estimator adjusted for bias is also included. Furthermore, alternative
moment-based estimation techniques such as the $L$-moment estimator and the
probability weighted moments estimator are included along with three different
minimum distance estimators. The finite sample performances of each of these
estimators is compared via an extensive Monte Carlo study. We find that no
single estimator outperforms its competitors uniformly. We recommend one of the
minimum distance estimators for use with smaller samples, while a bias reduced
version of maximum likelihood estimation is recommended for use with larger
samples. In addition, the desirable asymptotic properties of traditional
maximum likelihood estimators make them appealing for larger samples. We also
include a practical application demonstrating the use of the techniques on
observed data.
