Goodness—of—fit for the two—parameter weibull distribution with estimated parameters

1990 ◽  
Vol 34 (2-3) ◽  
pp. 133-143 ◽  
Author(s):  
Patricia J. Wozniak ◽  
Xiaozhu Li
2013 ◽  
Vol 58 (4) ◽  
pp. 1045-1052 ◽  
Author(s):  
A. Cias ◽  
A. Czarski

Abstract Low carbon ferro-manganese and graphite powders were admixed to Hoganas sponge, NC100.24, and water atomised, ABC 100.30 and ASC 100.29, iron powders - to produce three variants of sintered Fe-3Mn-0.8C steel. These were pressed into tensile and bend specimens at 660 MPa, sintered in semi-closed containers for 1 hour in dry nitrogen or hydrogen at 1120 or 1250°C and cooled at 64°C/min. Both tensile strength and transverse rupture strength were examined using Weibull statistics. This paper presents the results of a study to develop and evaluate goodness of fit tests for the two- and three-parameter Weibull distributions. The study was initiated because of discrepancies in published critical values for two-parameter Weibull distribution goodness of fit tests and the lack of general three-parameter Weibull distribution goodness of fit tests for properties of PM steels.


2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.


Author(s):  
Geum-Hee Jeong ◽  
Mi Kyoung Yim

To test the applicability of item response theory (IRT) to the Korean Nurses' Licensing Examination (KNLE), item analysis was performed after testing the unidimensionality and goodness-of-fit. The results were compared with those based on classical test theory. The results of the 330-item KNLE administered to 12,024 examinees in January 2004 were analyzed. Unidimensionality was tested using DETECT and the goodness-of-fit was tested using WINSTEPS for the Rasch model and Bilog-MG for the two-parameter logistic model. Item analysis and ability estimation were done using WINSTEPS. Using DETECT, Dmax ranged from 0.1 to 0.23 for each subject. The mean square value of the infit and outfit values of all items using WINSTEPS ranged from 0.1 to 1.5, except for one item in pediatric nursing, which scored 1.53. Of the 330 items, 218 (42.7%) were misfit using the two-parameter logistic model of Bilog-MG. The correlation coefficients between the difficulty parameter using the Rasch model and the difficulty index from classical test theory ranged from 0.9039 to 0.9699. The correlation between the ability parameter using the Rasch model and the total score from classical test theory ranged from 0.9776 to 0.9984. Therefore, the results of the KNLE fit unidimensionality and goodness-of-fit for the Rasch model. The KNLE should be a good sample for analysis according to the IRT Rasch model, so further research using IRT is possible.


Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.


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