Handbook of Tables for Order Statistics from Lognormal Distributions with Applications

Lognormal distributions are one of the most commonly studied models in the sta- tistical literature while being most frequently used in the applied literature. The lognormal distributions have been used in problems arising from such diverse fields as hydrology, biology, communication engineering, environmental science, reliability, agriculture, medical science, mechanical engineering, material science, and pharma- cology. Though the lognormal distributions have been around from the beginning of this century (see Chapter 1), much of the work concerning inferential methods for the parameters of lognormal distributions has been done in the recent past. Most of these methods of inference, particUlarly those based on censored samples, involve extensive use of numerical methods to solve some nonlinear equations. Order statistics and their moments have been discussed quite extensively in the literature for many distributions. It is very well known that the moments of order statistics can be derived explicitly only in the case of a few distributions such as exponential, uniform, power function, Pareto, and logistic. In most other cases in- cluding the lognormal case, they have to be numerically determined. The moments of order statistics from a specific lognormal distribution have been tabulated ear- lier. However, the moments of order statistics from general lognormal distributions have not been discussed in the statistical literature until now primarily due to the extreme computational complexity in their numerical determination.

Lognormal distributions are one of the most commonly studied models in the sta- tistical literature while being most frequently used in the applied literature. The lognormal distributions have been used in problems arising from such diverse fields as hydrology, biology, communication engineering, environmental science, reliability, agriculture, medical science, mechanical engineering, material science, and pharma- cology. Though the lognormal distributions have been around from the beginning of this century (see Chapter 1), much of the work concerning inferential methods for the parameters of lognormal distributions has been done in the recent past. Most of these methods of inference, particUlarly those based on censored samples, involve extensive use of numerical methods to solve some nonlinear equations. Order statistics and their moments have been discussed quite extensively in the literature for many distributions. It is very well known that the moments of order statistics can be derived explicitly only in the case of a few distributions such as exponential, uniform, power function, Pareto, and logistic. In most other cases in- cluding the lognormal case, they have to be numerically determined. The moments of order statistics from a specific lognormal distribution have been tabulated ear- lier. However, the moments of order statistics from general lognormal distributions have not been discussed in the statistical literature until now primarily due to the extreme computational complexity in their numerical determination.