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A Study of Fitting the Generalized Lambda Distribution to Solar Radiation Data

A. ÖztürkDepartment of Agronomy, Purdue University, West Lafayette, IN 47907

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R. F. DaleDepartment of Agronomy, Purdue University, West Lafayette, IN 47907

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Abstract

The increased interest in the climatology of solar radiation dictates a need for a distribution to fit daily solar radiation totals which tend to have negatively-skewed probability distributions. Even daily mean solar radiation for weekly periods tends to have non-normal distributions. The generalized lambda distribution, which includes a wide variety of curve shapes, is discussed for fitting these data. The underlying probability distribution is a generalization of the lambda distribution from three to four parameters. Using the weekly averages of daily solar radiation totals for each of 12 weeks during the growing season and daily totals for the week 5-11 July at West Lafayette, Indiana, it is shown that the generalized lambda distribution model fits the data well. Some results concerning percentiles and quantiles, parameter estimates, and goodness-of-fit tests are also discussed.

Abstract

The increased interest in the climatology of solar radiation dictates a need for a distribution to fit daily solar radiation totals which tend to have negatively-skewed probability distributions. Even daily mean solar radiation for weekly periods tends to have non-normal distributions. The generalized lambda distribution, which includes a wide variety of curve shapes, is discussed for fitting these data. The underlying probability distribution is a generalization of the lambda distribution from three to four parameters. Using the weekly averages of daily solar radiation totals for each of 12 weeks during the growing season and daily totals for the week 5-11 July at West Lafayette, Indiana, it is shown that the generalized lambda distribution model fits the data well. Some results concerning percentiles and quantiles, parameter estimates, and goodness-of-fit tests are also discussed.

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