FITTING A THREE-PARAMETER LOG-NORMAL DISTRIBUTION BY LEAST SQUARES

Least squares fitting the three - parameter inverse Weibull density ∗

The inverse Weibull model was developed by Erto [10]. In practice, the unknown parameters of the appropriate inverse Weibull density are not known and must be estimated from a random sample. Estimation of its parameters has been approached in the literature by various techniques, because a standard maximum likelihood estimate does not exist. To estimate the unknown parameters of the three-param...

On nonlinear weighted least squares fitting of the three-parameter inverse Weibull distribution∗

In this paper we consider nonlinear least squares fitting of the three-parameter inverse Weibull distribution to the given data (wi, ti, yi), i = 1, . . . , n, n ≥ 3. As the main result, we show that the least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) 0 < t1 < t2 < . . . < tn and (ii) 0 < y1 < y2 < . . . < yn < 1. To this end, an illus...

PEDOMODELS FITTING WITH FUZZY LEAST SQUARES REGRESSION

Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...

Fitting Distances by Least Squares

Fitting the Three-parameter Weibull Distribution by using Greedy Randomized Adaptive Search Procedure

The Weibull distribution is widely employed in several areas of engineering because it is an extremely flexible distribution with different shapes. Moreover, it can include characteristics of several other distributions. However, successful usage of Weibull distribution depends on estimation accuracy for three parameters of scale, shape and location. This issue shifts the attentions to the requ...