A neural network applied to estimate Burr XII distribution parameters

The Burr XII distribution can closely approximate many other well-known probability density functions such as the normal, gamma, lognormal, exponential distributions as well as Pearson type I, II, V, VII, IX, X, XII families of distributions. Considering a wide range of shape and scale parameters of the Burr XII distribution, it can have an important role in reliability modeling, risk analysis and process capability estimation. However, estimating parameters of the Burr XII distribution can be a complicated task and the use of conventional methods such as maximum likelihood estimation (MLE) and moment method (MM) is not straightforward. Some tables to estimate Burr XII parameters have been provided by Burr (1942) [1] but they are not adequate for many purposes or data sets. Burr tables contain specific values of skewness and kurtosis and their corresponding Burr XII parameters. Using interpolation or extrapolation to estimate other values may provide inappropriate estimations. In this paper, we present a neural network to estimate Burr XII parameters for different values of skewness and kurtosis as inputs. A trained network is presented, and one can use it without previous knowledge about neural networks to estimate Burr XII distribution parameters. Accurate estimation of the Burr parameters is an extension of simulation studies.

[1]  Dallas R. Wingo,et al.  Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data , 1993 .

[2]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[3]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[4]  Chao-Yu Chou,et al.  Economic-statistical design of X ¥ charts for non-normal data by considering quality loss , 2000 .

[5]  D. R. Wingo,et al.  Maximum Likelihood Methods for Fitting the Burr Type XII Distribution to Life Test Data , 1983 .

[6]  Irving W. Burr,et al.  Pameters for a general system of distributions to match a grid of α3 and α4 , 1973 .

[7]  Babak Abbasi,et al.  A neural network applied to estimate process capability of non-normal processes , 2009, Expert Syst. Appl..

[8]  M. E. Ghitany,et al.  Maximum likelihood estimation of Burr XII distribution parameters under random censoring , 2002 .

[9]  I. W. Burr.  Cumulative Frequency Functions , 1942 .

[10]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[11]  Fu-Kwun Wang,et al.  Maximum likelihood estimation of the Burr XII parameters with censored and uncensored data , 1996 .

[12]  W. Härdle,et al.  Statistical Tools for Finance and Insurance , 2003 .

[13]  Pandu R. Tadikamalla,et al.  A Look at the Burr and Related Distributioni , 1980 .

[14]  Z. F. Jaheen,et al.  Statistical inference for the Burr model based on progressively censored data , 2002 .

[15]  Sergey Lvin,et al.  Analysis op failure time data by burr distribution , 1996 .

[16]  Robert N. Rodriguez.  A guide to the Burr type XII distributions , 1977 .

[17]  J. Bert Keats,et al.  The Burr XII Distribution in Reliability Analysis , 1998 .