scholarly journals PROBABILITY DISTRIBUTION OF TIME DURATION OF MANUAL OPERATION IN THE PRODUCTION OF GLASS EYES

2021 ◽  
Vol 11 (2) ◽  
pp. 340-342
Author(s):  
VLADIMIR SOJKA ◽  
PETR LEPSIK
Keyword(s):  
Probability Distribution ◽  
Capacity Planning ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Time Duration ◽  
Manual Operation ◽  
Precise Data ◽  
Duration Distribution ◽  
Use Values

When precise planning of capacities and times of production is needed, there must be precise data for calculation. Not all operations have to have a normal time duration distribution. Counting with average values or use values from guessed distribution can lead to mistakes in actual production planning. This article aims to determine time probability distributions to manual operations. Tests of goodness of fit are used to search for more suitable distributions. This approach is presented in a case study of glass eyes manufacturing. Results show that there can be differences between the estimated normal distribution and another more suitable one. By using tests of goodness of fit to define the correct distribution, more precise production and capacity planning results can be achieved.

scholarly journals A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

2016 ◽  
Vol 11 (1) ◽  
pp. 432-440 ◽  
Author(s):  
M. T. Amin ◽  
M. Rizwan ◽  
A. A. Alazba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Future Research ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Northern Regions ◽  
Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

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.

scholarly journals Best Fitted Distribution For Meteorological Data In Kuala Krai

2021 ◽  
Vol 3 (1) ◽  
pp. 16-25
Author(s):  
Siti Mariam Norrulashikin ◽  
Fadhilah Yusof ◽  
Siti Rohani Mohd Nor ◽  
Nur Arina Bazilah Kamisan
Keyword(s):  
Climate Change ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Meteorological Data ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Data Series ◽  
Distribution Models ◽  
Goodness Of Fit Tests

Modeling meteorological variables is a vital aspect of climate change studies. Awareness of the frequency and magnitude of climate change is a critical concern for mitigating the risks associated with climate change. Probability distribution models are valuable tools for a frequency study of climate variables since it measures how the probability distribution able to fit well in the data series. Monthly meteorological data including average temperature, wind speed, and rainfall were analyzed in order to determine the most suited probability distribution model for Kuala Krai district. The probability distributions that were used in the analysis were Beta, Burr, Gamma, Lognormal, and Weibull distributions. To estimate the parameters for each distribution, the maximum likelihood estimate (MLE) was employed. Goodness-of-fit tests such as the Kolmogorov-Smirnov, and Anderson-Darling tests were conducted to assess the best suited model, and the test's reliability. Results from statistical studies indicate that Burr distributions better characterize the meteorological data of our research. The graph of probability density function, cumulative distribution function as well as Q-Q plot are presented.

scholarly journals Best fitting probability distributions for annual maximum discharge data of the river Kopili, Assam

2009 ◽  
Vol 1 (1) ◽  
pp. 50-52
Author(s):  
Abhijit Bhuyan ◽  
Munindra Borah
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Annual Maximum ◽  
Discharge Data ◽  
Generalized Pareto ◽  
Maximum Discharge ◽  
Pearson Type ◽  
Best Fitting ◽  
Log Normal

In this study our main objective is to determine the best fitting probability distribution for annual maximum flood discharge data of river Kopili, Assam. Various probability distributions i.e. Gumbel (G), generalized extreme value (GEV), normal (N), log-normal (LN3), generalized logistic (GLO), generalized pareto (GPA) and Pearson type-III (PE3) have been used for our study. The L-moments methods have been used for estimating the parameters of all the distributions. The root mean square error (RMSE), model efficiency and D-index (fit in the top six values) together with L-moment ratio diagram is used for goodness of fit measure. It has been observed that Generalized Pareto is the best fitting probability distribution for annual maximum discharge data of river Kopili.

scholarly journals Fitting of Probability Distribution on the Post-Monsoon Rainfall of Different Locations in Bangladesh

2019 ◽  
Vol 9 (2) ◽  
pp. 27
Author(s):  
Md. Habibur Rahman
Keyword(s):  
Probability Distribution ◽  
Weibull Distribution ◽  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Monsoon Rainfall ◽  
Probability Distributions ◽  
Monsoon Precipitation ◽  
Post Monsoon

Different probability distributions of post-monsoon rainfall of different locations in Bangladesh are fitted. It is found that, for the data, Weibull distribution for Barisal, Bogra, Chittagong, Comilla, Cox's Bazar, Faridpur, Jessore, Khulna, Maijdi Court, Mymensingh, Satkhira, and Sylhet; the Gamma distribution for Dhaka, Ishurdi, Rangamati, Rangpur, and Srimangal based on graphical assessment and goodness-of-fit criterion. In this study, different probability distributions have been fitted for the data of post-monsoon precipitation for 17 different locations in Bangladesh over the period 1961-2014.

scholarly journals Probability Distribution for the Visually Observed Fractional Cloud Cover over the Ocean

2018 ◽  
Vol 31 (8) ◽  
pp. 3207-3232 ◽  
Author(s):  
Marina Aleksandrova ◽  
Sergey K. Gulev ◽  
Konstantin Belyaev
Keyword(s):  
Probability Distribution ◽  
Cloud Cover ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
World Ocean ◽  
Accurate Estimation ◽  
Fractional Cloud ◽  
Low Cloud ◽  
Different Shapes ◽  
Low Cloud Cover

Abstract The authors suggest a three-parameter bounded distribution from the family of mixed gamma distributions for characterizing the probability density distributions of fractional total and low cloud cover over the global oceans. The authors derive both the continuous form of this distribution and its discrete counterpart, which can be directly applied to cloud cover reports. The distribution is applied to the cloud cover characteristics reported by voluntary observing ships (VOS) for the period from 1950 to 2011 after filtering nighttime observations with poor lunar illumination. The suggested distribution demonstrates a high goodness of fit to the data and good skill in capturing probability distributions with different shapes. The authors present seasonal climatologies of the parameters of the derived distribution for the chosen 60-yr period and demonstrate that applying the PDF-based concept to the analysis of cloud cover allows identification of areas where similar mean cloud amounts can be produced by probability distributions with very different shapes. The roles of the different parameters of the distribution in producing the observed cloud conditions in different regions of the World Ocean are discussed. The application of the derived probability distribution allows for accurate estimation of the percentiles of the distribution, which represent the probabilities of specific cloud conditions. These probabilities are presented for both total and low cloud cover, as well as for daytime and nighttime. The authors also discuss the applicability of the suggested distribution for the validation of different cloud cover data products over the globe and the prospects of additional applications.

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 17 (11) ◽  
pp. 4541-4553 ◽  
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Functions ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Distribution Fitting ◽  
Distribution Method ◽  
Wide Variability ◽  
Anderson Darling

Abstract. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall–runoff models. The use of representative single values of hydrological losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. The probability distribution method is potentially a better technique to describe losses. However, a lack of understanding of how losses are distributed can limit the use of this technique. This paper aims to identify a probability distribution function that can successfully describe hydrological losses of a catchment of interest. The paper explains the systematic process of identifying probability distribution functions, the problems faced during the distribution fitting process and a new generalised method to test the adequacy of fitted distributions. The goodness-of-fit of the fitted distributions are examined using the Anderson–Darling test and the Q–Q plot method and the errors associated with quantile estimation are quantified by estimating the bias and mean square error (MSE). A two-parameter gamma distribution was identified as one that successfully describes initial loss (IL) data for the selected catchments. Further, non-parametric standardised distributions that describe both IL and continuing loss data are also identified. This paper will provide a significant contribution to the Australian Rainfall and Runoff (ARR) guidelines that are currently being updated, by improving understanding of hydrological losses in South Australian catchments. More importantly, this study provides new knowledge on how IL in a catchment is characterised.

scholarly journals Establishment of a Stochastic Model for Sustainable Economic Flood Management in Yewa Sub-Basin, Southwest Nigeria

2016 ◽  
Vol 2 (12) ◽  
pp. 646-655 ◽  
Author(s):  
O.A Agbede ◽  
Oluwatobi Aiyelokun
Keyword(s):  
Probability Distribution ◽  
Stochastic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Flood Management ◽  
Return Periods ◽  
Probability Models ◽  
Goodness Of Fit Test ◽  
Southwest Nigeria ◽  
Anderson Darling

Of all natural disasters, floods have been considered to have the greatest potential damage. The magnitude of economic damages and number of people affected by flooding have recently increased globally due to climate change. This study was based on the establishment of a stochastic model for reducing economic floods risk in Yewa sub-basin, by fitting maximum annual instantaneous discharge into four probability distributions. Daily discharge of River Yewa gauged at Ijaka-Oke was used to establish a rating curve for the sub-basin, while return periods of instantaneous peak floods were computed using the Hazen plotting position. Flood magnitudes were found to increase with return periods based on Hazen plotting position. In order to ascertain the most suitable probability distribution for predicting design floods, the performance evaluation of the models using root mean square error was employed. In addition, the four probability models were subjected to goodness of fit test besed on Anderson-Darling (A2) and Kolmogorov-Smirnov (KS). As a result of the diagnostics test the Weibul probability distribution was confirmed to fit well with the empirical data of the study area. The stochastic model  generated from the Weibul probability distribution, could be used to enhance sustainable development by reducing economic flood damages in the sub-basin.

scholarly journals Distribution of Earthquake Magnitude Levels in Bangladesh

2019 ◽  
Vol 11 (3) ◽  
pp. 15
Author(s):  
Md. Habibur Rahman ◽  
Md. Moyazzem Hossain
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Earthquake Magnitude ◽  
Human Beings ◽  
Richter Scale ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Best Fit

Earthquakes are one of the main natural hazards which seriously make threats the life and property of human beings. Different probability distributions of the earthquake magnitude levels in Bangladesh are fitted. In terms of graphical assessment and goodness-of-fit criterion, the log-normal distribution is found to be the best fit probability distributions for the earthquake magnitude levels in Bangladesh among the probability distribution considered in this study. The average earthquake magnitude level found 4.67 (in Richter scale) for log-normal distribution and the approximately forty-six percent chance is predicted to take place earthquake magnitude in the interval four to five.

scholarly journals Selection Selection of Probabilistic Model of Extreme Floods in Benue River Basin, Nigeria

2021 ◽  
Vol 6 (1) ◽  
pp. 7-18
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
River Basin ◽  
Frequency Analysis ◽  
Probabilistic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Extreme Floods ◽  
Pearson Type ◽  
Selection Of

The selection of optimum probabilistic model of extreme floods as a crucial step for flood frequency analysis has remained a formidable challenge for the scientific and engineering communities to address. Presently, there is no scientific consensus about the choice of probability distribution model that would accurately simulate flood discharges at a particular location or region. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the design quantile - probability relationship. This paper presents the evaluation of five probability distributions models; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalized Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of four hydrological stations in Benue River Basin in Nigeria. Additionally, Q-Q plots were used to compliment the selection process. The choice of optimum probability distribution model was based on five statistical goodness – of – fit measures; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR). Goodness – of – fit assessment reveals that GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. In comparison with WMO (1989) survey of countries on distribution types currently in use for frequency analysis of extremes of floods shows that GEV is standard in one country, while PR3 is a standard in 7 countries, and LP3 is standard in 7 countries. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.

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