Some Inferential Results on a Two Parameter Generalized Half Normal Distribution

2021 ◽  
pp. 1-17
Author(s):  
Matinee Sudsawat ◽  
Nabendu Pal
Keyword(s):  
Normal Distribution ◽  
Two Parameter

A two-parameter generalized skew-normal distribution

2008 ◽  
Vol 78 (13) ◽  
pp. 1722-1726 ◽  
Author(s):  
A. Jamalizadeh ◽  
J. Behboodian ◽  
N. Balakrishnan
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Two Parameter ◽  
Skew Normal

scholarly journals Estimation on Reliability Models of Bearing Failure Data

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Xia Xintao ◽  
Chang Zhen ◽  
Zhang Lijun ◽  
Yang Xiaowei
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Normal Distribution ◽  
Distribution Model ◽  
Bearing Failure ◽  
Analysis Model ◽  
Failure Data ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Two Parameter

The failure data of bearing products is random and discrete and shows evident uncertainty. Is it accurate and reliable to use Weibull distribution to represent the failure model of product? The Weibull distribution, log-normal distribution, and an improved maximum entropy probability distribution were compared and analyzed to find an optimum and precise reliability analysis model. By utilizing computer simulation technology and k-s hypothesis testing, the feasibility of three models was verified, and the reliability of different models obtained via practical bearing failure data was compared and analyzed. The research indicates that the reliability model of two-parameter Weibull distribution does not apply to all situations, and sometimes, two-parameter log-normal distribution model is more precise and feasible; compared to three-parameter log-normal distribution model, the three-parameter Weibull distribution manifests better accuracy but still does not apply to all cases, while the novel proposed model of improved maximum entropy probability distribution fits not only all kinds of known distributions but also poor information issues with unknown probability distribution, prior information, or trends, so it is an ideal reliability analysis model with least error at present.

Error Distributions in Navigation

1972 ◽  
Vol 25 (2) ◽  
pp. 250-252 ◽  
Author(s):  
J. B. Parker
Keyword(s):  
Normal Distribution ◽  
Frequency Distributions ◽  
Families Of Curves ◽  
Pearson Type ◽  
Error Distributions ◽  
The One ◽  
Two Parameter

Graduating error distributions by families of curves has a long and distinguished history. In seeking a class of frequency distributions which graduate navigational data, Anderson and Ellis are motivated by the well-known shortcomings of the normal distribution which so often fails to do justice to the data in the tails of the distribution. They generalize the one parameter (σ) zero-mean gaussian family to a two parameter (α, β) family which is in fact the Pearson Type VII class. They then observe that this class graduates published navigational distributions very wells.

scholarly journals A Two-parameter Balakrishnan Skew-normal Distribution

2010 ◽  
Vol 6 (2) ◽  
pp. 231-242
Author(s):  
Wahab Bahrami ◽  
Hamzeh Agahi ◽  
Hojat Rangin ◽  
◽  
◽  
...  
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Two Parameter ◽  
Skew Normal

COMPARISON OF WEIBULL AND NORMAL PROBABILITY DISTRIBUTION OF FLEXURAL STRENGTH OF DENSE AND POROUS FIRED CLAY

2016 ◽  
Vol 78 (9) ◽  
Author(s):  
Muazu Abubakar ◽  
Muhamad Azizi Mat Yajid ◽  
Norhayati Ahmad
Keyword(s):  
Probability Distribution ◽  
Flexural Strength ◽  
Normal Distribution ◽  
Probability Distributions ◽  
Bending Test ◽  
Strength Data ◽  
Normal Probability ◽  
Distribution Parameters ◽  
Normal Probability Distribution ◽  
Two Parameter

In this research, dense and porous fired clay were produced at a firing temperature of 1300°C. The flexural strength data of the dense and the porous fired clay were determined using three point bending test. Two-parameter Weibull and normal probability distributions were used to estimate the reliability of the flexural strength data of the dense and the porous fired clay. From the result, the Weibull probability distribution scale parameter for the dense (36.31MPa) and Porous (18.85MPa) fired clay are higher than the mean strength value for the dense (33.84MPa) and the porous (17.87MPa) of the normal distribution. Distributions of flaws in the dense and the porous fired clay have a significant effect on the Weibull and normal distribution parameters. The fractured surface of the dense fired clay shows a random distribution of cracks while that of the porous fired clay shows a distribution of pores in the morphology. The normal distribution considers failure at 50% of the flexural strength data while Weibull probability distribution is failure at 62.3% of the strength data. Therefore, two-parameter Weibull is the suitable tool to model failure strength data of the dense and porous fired clay.  

scholarly journals Description of the statistical variations of the measured strength for brittle ceramics: A comparison between two-parameter Weibull distribution and normal distribution

2020 ◽  
Vol 14 (4) ◽  
pp. 293-302
Author(s):  
Bin Deng ◽  
Xingang Wang ◽  
Danyu Jiang ◽  
Jianghong Gong
Keyword(s):  
Weibull Distribution ◽  
Normal Distribution ◽  
Fracture Probability ◽  
Strong Correlations ◽  
Strength Data ◽  
Statistical Variations ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Two Parameter ◽  
Measured Strength

It is generally assumed that the measured strength of brittle ceramics follows a Weibull distribution. However, there seems to be few sound and direct evidences to support this assumption. Several previous studies have shown that other distributions, such as normal distribution and log-normal distribution may describe more appropriately the strength data than Weibull distribution. In this paper, the efficiency of using a normal distribution to describe the strength which follows a Weibull distribution is examined based on Monte-Carlo simulations. It was shown that there exist strong correlations between the parameters of normal distribution and those of Weibull distribution. For the designed fracture probability not lower than 0.01, analyses based on both normal distribution and Weibull distribution may give nearly identical predictions for the applicable stress levels. For lower fracture probabilities, the differences between the predictions of both distributions are not significant. It was suggested that, if there is no evidence to confirm that the measured strength follows a certain distribution, normal distribution and Weibull distribution seem to have the same efficiency in analysing the statistical variations in the measured strength of ceramics.

scholarly journals Estimating the mean of a small sample under the two parameter lognormal distribution

2018 ◽  
Vol 1 ◽  
pp. 100
Author(s):  
Peter Hingley
Keyword(s):  
Normal Distribution ◽  
Lognormal Distribution ◽  
Population Distribution ◽  
Model Misspecification ◽  
Small Sample ◽  
Maximum Likelihood Estimates ◽  
Sampling Distributions ◽  
The Mean ◽  
Normal Variance ◽  
Two Parameter

Lognormally distributed variables are found in biological, economic and other systems. Here the sampling distributions of maximum likelihood estimates (MLE) for parameters are developed when data are lognormally distributed and estimation is carried out either by the correct lognormal model or by the mis-specified normal distribution. This is designed as an aid to experimental design when drawing a small sample under an assumption that the population follows a normal distribution while in fact it follows a lognormal distribution. Distributions are derived analytically as far as possible by using a technique for estimator densities and are confirmed by simulations. For an independently and identically distributed lognormal sample, when a normal distribution is used for estimation then the distribution of the MLE of the mean is different to that for the MLE of the lognormal mean. The distribution is not known but can be well enough approximated by another lognormal. An analytic method for the distribution of the mis-specified normal variance uses computational convolution for a sample of size 2. The expected value of the mis-specified normal variance is also found as a way to give information about the effect of the model misspecification on inferences for the mean. The results are demonstrated on an example for a population distribution that is abstracted from a survey.

Some results of the Barbier-Chalonge-Divan system of stellar classification

1966 ◽  
Vol 24 ◽  
pp. 77-90 ◽  
Author(s):  
D. Chalonge
Keyword(s):  
Early Type ◽  
Parameter System ◽  
Early Type Stars ◽  
Two Parameter

Several years ago a three-parameter system of stellar classification has been proposed (1, 2), for the early-type stars (O-G): it was an improvement on the two-parameter system described by Barbier and Chalonge (3).

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