Graphical representations and associated goodness-of-fit tests for Pareto and log-normal distributions based on inequality curves

2021 ◽  
pp. 1-18
Author(s):  
Emanuele Taufer ◽  
Flavio Santi ◽  
Giuseppe Espa ◽  
Maria Michela Dickson
Keyword(s):  
Goodness Of Fit ◽  
Graphical Representations ◽  
Normal Distributions ◽  
Goodness Of Fit Tests ◽  
Log Normal

scholarly journals Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

Modeling the Uncertainty of Surgical Procedure Times

2000 ◽  
Vol 92 (4) ◽  
pp. 1160-1167 ◽  
Author(s):  
David P. Strum ◽  
Jerrold H. May ◽  
Luis G. Vargas
Keyword(s):  
Surgical Procedure ◽  
Goodness Of Fit ◽  
Statistical Tests ◽  
Current Procedural Terminology ◽  
Normal Model ◽  
Rounding Errors ◽  
Goodness Of Fit Tests ◽  
Time Estimates ◽  
Surgical Scheduling ◽  
Log Normal

Background Medical institutions are under increased economic pressure to schedule elective surgeries efficiently to contain the costs of surgical services. Surgical scheduling is complicated by variability inherent in the duration of surgical procedures. Modeling that variability, in turn, provides a mechanism to generate accurate time estimates. Accurate time estimates are important operationally to improve operating room utilization and strategically to identify surgeons, procedures, or patients whose duration of surgeries differ from what might be expected. Methods The authors retrospectively studied 40,076 surgical cases (1,580 Current Procedural Terminology-anesthesia combinations, each with a case frequency of five or more) from a large teaching hospital, and attempted to determine whether the distribution of surgical procedure times more closely fit a normal or a log-normal distribution. The authors tested goodness-of-fit to these data for both models using the Shapiro-Wilk test. Reasons, in practice, the Shapiro-Wilk test may reject the fit of a log-normal model when in fact it should be retained were also evaluated. Results The Shapiro-Wilk test indicates that the log-normal model is superior to the normal model for a large and diverse set of surgeries. Goodness-of-fit tests may falsely reject the log-normal model during certain conditions that include rounding errors in procedure times, large sample sizes, untrimmed outliers, and heterogeneous mixed populations of surgical procedure times. Conclusions The authors recommend use of the log-normal model for predicting surgical procedure times for Current Procedural Terminology-anesthesia combinations. The results help to legitimize the use of log transforms to normalize surgical procedure times before hypothesis testing using linear statistical models or other parametric statistical tests to investigate factors affecting the duration of surgeries.

Characterizations of normal distributions and EDF goodness-of-fit tests

Metrika ◽  
2003 ◽  
Vol 58 (2) ◽  
pp. 149-157 ◽  
Author(s):  
Truc T. Nguyen ◽  
Khoan T. Dinh
Keyword(s):  
Goodness Of Fit ◽  
Normal Distributions ◽  
Goodness Of Fit Tests

Comparison of Weibull and normal distributions for concrete compressive strengths

2006 ◽  
Vol 33 (10) ◽  
pp. 1287-1292 ◽  
Author(s):  
P J Tumidajski ◽  
L Fiore ◽  
T Khodabocus ◽  
M Lachemi ◽  
R Pari
Keyword(s):  
Compressive Strength ◽  
Weibull Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Theoretical Description ◽  
Normal Distributions ◽  
Failure Data ◽  
Goodness Of Fit Tests ◽  
Strength Failure ◽  
The Difference

For concrete produced in a commercial ready mix operation, the compressive strengths were fitted to Weibull and normal distributions. It was found that the Weibull distribution successfully describes concrete compressive strength failure data. This information is useful in the theoretical description of concrete failure. Furthermore, based on chi-squared, Anderson–Darling and Kolmogorov-Smirnov goodness-of-fit tests, the difference between the Weibull and normal distribution is not large enough to make a clear distinction regarding which distribution definitively fits the experimental data better. Key words: compressive strength, normal distribution, Weibull distribution, goodness-of-fit.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

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