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A neural network applied to estimate Burr XII distribution parameters

Abbasi, B ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ress.2010.02.001
  3. Publisher: 2010
  4. Abstract:
  5. 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
  6. Keywords:
  7. Burr XII distribution ; Accurate estimation ; Artificial Neural Network ; Conventional methods ; Data sets ; Distribution parameters ; Estimating parameters ; Exponential distributions ; Log-normal ; Moment methods ; Process capabilities ; Reliability modeling ; Scale parameter ; Simulation studies ; Specific values ; Approximation theory ; Distribution functions ; Exponential functions ; Maximum likelihood estimation ; Neural networks ; Probability density function ; Reliability analysis ; Risk analysis ; Risk assessment ; Risk perception ; Safety factor ; Parameter estimation
  8. Source: Reliability Engineering and System Safety ; Volume 95, Issue 6 , June , 2010 , Pages 647-654 ; 09518320 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0951832010000360?np=y&npKey=d40ac8d139ca08da094d0bdecb5681c2dbe2f768c64ccca60ce8158ef6c644f4