The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters

Statistical analysis of residual stress determinations using neutron diffraction

“…In the analyses used here, the probability distributions resulting from Eq. (10) were fitted with a 'Pearson IV' curve [15] which can approximate to a symmetrical Gaussian as well as an asymmetrical distribution. The output values obtained in each case were the centre value (the largest probability), the centroid value (the centre of mass of the distribution) and the Full Width at Half Maximum (FWHM).…”

Econometric modeling and value-at-risk using the Pearson type-IV distribution

“…(2) are real, by rearranging the terms we conclude on the Pearson type-IV distribution in its recent form (Nagahara, 1999):…”

“…Due to the mathematical difficulty, the computational complexity, and the fact that the information regarding this distribution is scattered in the literature, the system has not yet attracted attention in the econometric literature since, to keep the ARCH tradition it is important to express the density in terms of the mean and of the variance, in order to acquire a distribution with zero mean and unit variance. According to Pearson (1895) and Nagahara (1999Nagahara ( , 2004Nagahara ( , 2007 the normalization constant is given by:…”

Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US

“…In the area of financial engineering, the Pearson type VII and IV distributions were used for the error term of the ARCH-like models of time series data of stock returns (Nagahara 1995;Premaratne and Bera 2001;Verhoeven and McAleer 2003), the return distributions of stock index and its diffusion (Nagahara 1996) and the stochastic volatility models (Nagahara and Kitagawa 1999). Furthermore, the author overcomed various difficulties of the Pearson type IV distribution for the practical usage and estimated the parameters for the stock returns by maximum likelihood method (Nagahara 1999). And the characteristic function of the Pearson type IV distribution is introduced by Kotz and Nagahara (2001), and Baldi et al (2001), independently.…”