Identifying a Two-Parameter Distribution by the First two Sample Moment (Partial and Complete)

1995 ◽  
Vol 52 (1) ◽  
pp. 17-32 ◽  
Author(s):  
Haim. Shore
Keyword(s):  
Parameter Distribution ◽  
Sample Moment ◽  
Two Parameter

scholarly journals A New Extended Two-Parameter Distribution: Properties, Estimation Methods, and Applications in Medicine and Geology

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1578 ◽  
Author(s):  
Hazem Al-Mofleh ◽  
Ahmed Z. Afify ◽  
Noor Akma Ibrahim
Keyword(s):  
Estimation Method ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Proposed Model ◽  
Rate Functions ◽  
The Mean ◽  
Modeling Data ◽  
Two Parameter

In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall–Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson–Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

scholarly journals Behaviour of spatial rainfall correlation For short distances

MAUSAM ◽  
2021 ◽  
Vol 43 (3) ◽  
pp. 269-272
Author(s):  
J. N. KANAUJIA ◽  
SURINDER KAUR ◽  
D. S. Upadhyay
Keyword(s):  
Theoretical Model ◽  
Missing Data ◽  
Network Design ◽  
Short Distance ◽  
Annual Rainfall ◽  
Parameter Distribution ◽  
Data Interpolation ◽  
Areal Rainfall ◽  
Transfer Of Information ◽  
Two Parameter

The correlation between two series of rainfall recorded at two stations which are at short distance, is usually found significant. This information has important applicability in the areas of data interpolation, network design, transfer of information in respect of missing data and deriving areal rainfall from point values. In this paper 70-year (1901-1970) annual rainfall data for about 1500 stations in India have been analysed. The distribution of correlation coefficient (r) for the stations located within a distance of 40 km were obtained. Attempt has been made to derive theoretical model of r. For this purpose two distributions, (1) a two parameter -distribution and (2) a two parameter bounded distribution, have been chosen as in both cases the variable ranges from 0 to 1.  

scholarly journals Modelling the COVID-19 Mortality Rate with a New Versatile Modification of the Log-Logistic Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Abdisalam Hassan Muse ◽  
Ahlam H. Tolba ◽  
Eman Fayad ◽  
Ola A. Abu Ali ◽  
M. Nagy ◽  
...  
Keyword(s):  
Mortality Rate ◽  
Goodness Of Fit ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Logistic Distribution ◽  
Parameter Distribution ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
Competing Models ◽  
Two Parameter

The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.

Reliability Analysis of the Home and Abroad CNC Equipment Used in Automobile Parts Industry

2014 ◽  
Vol 651-653 ◽  
pp. 802-807
Author(s):  
Bin Ma ◽  
Min Luo ◽  
Zhi Chu Chen ◽  
Li Xin Cao
Keyword(s):  
Weibull Distribution ◽  
Empirical Distribution Function ◽  
Least Squares Method ◽  
Empirical Distribution ◽  
Distribution Model ◽  
Parameter Distribution ◽  
Linear Parameter ◽  
Auto Parts ◽  
Fault Information ◽  
Two Parameter

Through analyzing fault information of the home and abroad CNC equipment used in the same auto parts production, the fault data fitting were implemented in this paper. Assuming time between failure probability density function and the empirical distribution function follow the Weibull distribution, A reliability statistical model was built using the least squares method and a linear parameter distribution model regression method. The linear correlation test and the Weibull distribution fault interval obtained show the fact that both the home and abroad equipment are subject to the two parameter Weibull distribution, and after calculating the three indexes of reliability assessment, a conclusion can be made that the reliability of domestic equipment in the study is slightly lower than that of foreign equipment.

Comparison of stochastic models of rainfall processes in mountainous climatic conditions

2010 ◽  
Vol 1 (2) ◽  
pp. 135-146
Author(s):  
J. Y. Lee ◽  
M. Y. Han ◽  
D. K. Kim ◽  
W. H. Ji
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Rainwater Harvesting ◽  
Daily Rainfall ◽  
Percentage Error ◽  
Parameter Distribution ◽  
Mountainous Region ◽  
Simpler Algorithm ◽  
Two Parameter ◽  
Mixed Exponential Distribution

The main objective of this work was to find a stochastic simulation model that was suitable for designing a rainwater harvesting system for agricultural water utilization and irrigation water in a mountainous region. Several models were applied using daily rainfall data from two sites (Gangneung and Daekwanreung) to assess the accuracy and suitability of the model for simulating the daily rainfall. The amount of rainfall for the mountainous region was well described by a two-parameter gamma distribution and performed better than other distributions. However, validation tests revealed that the annual mean absolute percentage error (MAPE) was more than 10% at both locations. This result was different from some previous research in which a three-parameter mixed-exponential distribution was well described. In addition, although the exponential distribution was also well described by a second-order expression, the use of a one-parameter distribution had a simpler algorithm than the two-parameter gamma distribution and the three-parameter mixed-exponential distribution.

scholarly journals One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 34-54
Author(s):  
Aris Alexopoulos
Keyword(s):  
Exponential Distribution ◽  
Relative Entropy ◽  
Real Data ◽  
Parameter Distribution ◽  
Sample Mean ◽  
Type Distribution ◽  
Two Parameter ◽  
New Distribution ◽  
Extra Parameter ◽  
Mathematical Characteristics

A new one-parameter distribution is presented with similar mathematical characteristics to the two parameter conventional Weibull. It has an estimator that only depends on the sample mean. The relative entropy with respect to the Weibull distribution is derived in order to examine the level of similarity between them. The performance of the new distribution is compared to the Weibull and in some cases the Gamma distribution using real data. In addition, the Exponential distribution is modified to include an extra parameter via a simple transformation using fractional mathematics. It will be shown that the modified version also exhibits Weibull characteristics for particular values of the second parameter.

Acoustic Emission at the Kinetic and Development of the Structural Defects under Deformation of Aluminum Alloy

2015 ◽  
Vol 1091 ◽  
pp. 119-124
Author(s):  
Oleg Bashkov ◽  
Roman Romashko ◽  
Sergey V. Panin ◽  
Tatiana Bashkova
Keyword(s):  
Acoustic Emission ◽  
Aluminum Alloy ◽  
Frequency Parameter ◽  
Structural Defects ◽  
Parameter Distribution ◽  
Distribution Analysis ◽  
Dislocation Mechanism ◽  
Deformation Stages ◽  
Ae Signals ◽  
Two Parameter

The paper presents the results of studies the deformation behavior of aluminium alloy D16 by acoustic emission (AE) method. The purpose of this study was to establish the deformation stages and deformation mechanisms at each stage. Studies were carried out on the samples of aluminum alloy D16 (analog 7075). This paper contains a method for the separation of AE signals. The method of AE sources identification based on the the two-parameter distribution analysis (frequency parameter Kfvs energy of AE signals). The frequency parameter Kf is based on wavelet transform of AE signals. Two-parameter distribution allows one to separate the AE signals emitted by dislocations from the signals of micro cracks. The investigation results allowed the various deformation stages to establish by the different types of AE signals. By the AE analysis shows the dislocation mechanism of hardening the aluminum alloyD16. The paper presents the results that characterize the influences of heat treatment and structural condition of aluminum alloy on the AE parameters.

scholarly journals Quantitative analysis of flow microfluorometric data for screening gynecologic cytology specimens.

1979 ◽  
Vol 27 (1) ◽  
pp. 536-544 ◽  
Author(s):  
M C Habbersett ◽  
M Shapiro ◽  
B Bunnag ◽  
I Nishiya ◽  
C Herman
Keyword(s):  
Nucleic Acid ◽  
Cell Population ◽  
Fluorescein Isothiocyanate ◽  
Staining Intensity ◽  
Parameter Distribution ◽  
Screening Performance ◽  
Versus Protein ◽  
Tree Algorithms ◽  
Abnormal Cells ◽  
Two Parameter

Gynecologic cytology specimens that included the entire spectrum of cervical cytology classification were stained with a combination of propidium iodide and fluorescein isothiocyanate, then analyzed using a flow microfluorometer to measure nucleic acid and protein content, respectively. Numerous descriptors of the resulting two parameter distribution (nucleic acid versus protein) were defined. These descriptors included assessment of the presence or absence of abnormal cells. They also included measures of the staining intensity and dispersion of the normal squamous cell population and the intensity of inflammatory response in the cell population. Relative percentages of inflammatory and epithelial cells were demonstrated to effect the screening performance of this system only in borderline lesions. Decision tree algorithms allowed optimization of the selected parameters for screening logic of normal-abnormal decisions on a specimen-by-specimen basis. In addition, quantitative definitions of specimen adequacy were determined. Appropriate controls for batch staining of specimens were evaluated. These results of applying pattern recognition techniques to flow microfluorometer multiparameter data demonstrate that considerably more information about cell populations and subpopulations can be extracted than heretofore possible.

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