Technology for Calculating the Parameters of the Density Function of the Normal Distribution of the Useful Component in a Noisy Process

2016 ◽  
Vol 48 (4) ◽  
pp. 39-55 ◽  
Author(s):  
Telman Abbas ogly Aliev ◽  
Naila Fuad kyzy Musaeva ◽  
Matanat Tair kyzy Suleymanova ◽  
Bahruz Ismail ogly Gazizade
Keyword(s):  
Normal Distribution ◽  
Density Function

Analytical Representation of the Density Function of Normal Distribution of Noise

2015 ◽  
Vol 47 (8) ◽  
pp. 24-40 ◽  
Author(s):  
Telman Abbas ogly Aliev ◽  
Naila F. Musaeva ◽  
Matanat Tair kyzy Suleymanova ◽  
Bahruz Ismail ogly Gazizade
Keyword(s):  
Normal Distribution ◽  
Density Function ◽  
Analytical Representation

Probability Distribution of Tidal Elevation Data around Korean Coasts

2013 ◽  
Vol 284-287 ◽  
pp. 1484-1488
Author(s):  
Hong Yeon Cho ◽  
Shin Taek Jeong ◽  
Dong Hui Ko ◽  
Sang Ho Lee
Keyword(s):  
Normal Distribution ◽  
Density Function ◽  
Optimal Parameter ◽  
Kernel Functions ◽  
Normal Distribution Function ◽  
Tidal Elevation ◽  
Significance Level ◽  
Normality Test ◽  
Elevation Data

Frequency information of tidal elevations in the coastal zone is essential for the determination of datum level, the classification of inhabitation zones, and the analysis of mean sea level variation. In this study, the non-parametric density function is suggested for the analysis of hourly tidal elevation data provided by the Korea Hydrographic and Oceanographic Administration. The density function was estimated for six principal locations, Incheon, Mokpo, Jeju, Yeosu, Busan, and Pohang in the Korean coastal area using a kernel function. The parameter required for the probability density function was optimally estimated with the Sheather and Jones (SJ). And the optimal parameter appropriate for the normal distribution function was about 30% higher than that predicted by the SJ method or the Cross Validation (CV) method. It can be seen that the final kernel functions were less affected. The smoothing parameters for all of the tidal elevation data were optimized to be in the range of 0.13-0.17 with the SJ method. From the normality test of the observed tidal elevation data, it was proposed that the hypothesis of a normal distribution was inappropriate in the test techniques with a 95% significance level.

THE GENERALIZED BIPARABOLIC DISTRIBUTION

2009 ◽  
Vol 17 (03) ◽  
pp. 377-396 ◽  
Author(s):  
CATALINA BEATRIZ GARCÍA GARCÍA ◽  
JOSÉ GARCÍA PÉREZ ◽  
SALVADOR CRUZ RAMBAUD
Keyword(s):  
Normal Distribution ◽  
Closed Form ◽  
Density Function ◽  
Beta Distribution ◽  
Cumulative Density Function ◽  
Moment Ratio ◽  
Tsp Distribution ◽  
Mean Variance ◽  
Skewness And Kurtosis ◽  
Moment Ratio Diagram

Beta distributions have been applied in a variety of fields in part due to its similarity to the normal distribution while allowing for a larger flexibility of skewness and kurtosis coverage when compared to the normal distribution. In spite of these advantages, the two-sided power (TSP) distribution was presented as an alternative to the beta distribution to address some of its short-comings, such as not possessing a cumulative density function (cdf) in a closed form and a difficulty with the interpretation of its parameters. The introduction of the biparabolic distribution and its generalization in this paper may be thought of in the same vein. Similar to the TSP distribution, the generalized biparabolic (GBP) distribution also possesses a closed form cdf, but contrary to the TSP distribution its density function is smooth at the mode. We shall demonstrate, using a moment ratio diagram comparison, that the GBP distribution provides for a larger flexibility in skewness and kurtosis coverage than the beta distribution when restricted to the unimodal domain. A detailed mean-variance comparison of GBP, beta and TSP distributions is presented in a Project Evaluation and Review Technique (PERT) context. Finally, we shall fit a GBP distribution to an example of financial European stock data and demonstrate a favorable fit of the GBP distribution compared to other distributions that have traditionally been used in that field, including the beta distribution.

Research Lifetime of Oil Film Bearing on High-Speed Wire Mill Based on Reliability Analysis

2011 ◽  
Vol 402 ◽  
pp. 358-361
Author(s):  
Shi Bo Jiang ◽  
Jie Liu ◽  
Jun Lin Ten
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Reliability Analysis ◽  
Density Function ◽  
High Speed ◽  
Statistical Data ◽  
Wire Mill ◽  
Oil Film ◽  
Wear Life

Based on the prerequisite that oil- film Bearing wear extent obey normal distribution，This paper come to reliability account formula through wear extent probability density function，deduce the wear life account formula of oil- film Bearing. based on detailed statistical data, calculate the lifetime of oil film bearing in High Speed Wire Rod finishing block, and forward the method how to raise the lifetime of oil- film Bearing.

scholarly journals Probability Density Functions for Prediction Using Normal and Exponential Distribution

2021 ◽  
pp. 40-52
Author(s):  
Kunio Takezawa
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Density Function ◽  
Exponential Distribution ◽  
Predictive Ability ◽  
Probability Density Functions ◽  
Density Functions ◽  
Specific Distribution ◽  
Using Data

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

scholarly journals Port Equipment Downtime Prediction and Lifetime Data Analysis: Evidence from a Case Study

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Lot Okanminiwei ◽  
Sunday Ayoola Oke
Keyword(s):  
Normal Distribution ◽  
Density Function ◽  
Capital Expenditure ◽  
Container Terminal ◽  
Distribution Functions ◽  
Container Terminals ◽  
Lifetime Data ◽  
Southwestern Nigeria ◽  
The Mean ◽  
Gantry Cranes

Prediction of downtime and lifetime data for gantry cranes in a container terminal is a crucial concern for port terminals due to the requirement for maintenance planning and capital expenditure. Correct estimation of lifetime behavior for gantry cranes is complex since multiple cranes are involved, each with different costs, capacities; installation, and retirement dates. This paper develops statistically-oriented predictions for the lifetimes of container terminals company fleet of gantry cranes. Data records on downtime for cranes were collected and analyzed using Weibull, normal, and Rayleigh distributions regarding a port in southwestern Nigeria. The downtime, probability density function, cumulative density function, reliability, and hazard rate were analyzed for three shape functions of Weibull, β=0.5, 1, and 3. The same was analyzed for Rayleigh and normal distribution functions. The mean downtime was 30.58 hrs. The highest PDF, CDF, R(t) for all β =0.5, 1, and 3, were 0.26, 0.78, .030 and 13.13, respectively. However, the least values for these parameters are 0.01, 0.71, 0.25, and 0.04, respectively. These values are means for thirty data points and concern the Weibull distribution function. For the Rayleigh distribution, the mean PDF, CDF, R(t) and h(t) are 0.002, 0.042, 0.958 and 0.002 while they are 0.002, 0.456, 0.542 and 35.755 for the normal distribution. This article provides new insights into the lifetime analysis of gantry cranes in a container terminal.

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