scholarly journals Fracture Statistics Using Three-Parameter and Two-Parameter Weibull Distributions for Fe-0.4C-1.5Cr-1.5Ni-0.8Mn-0.2Mo Structural Sintered Steel

2016 ◽  
Vol 61 (3) ◽  
pp. 1547-1554 ◽  
Author(s):  
Ch. Fiał ◽  
A. Ciaś ◽  
A. Czarski ◽  
M. Sułowski
Keyword(s):  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Sufficient Evidence ◽  
Parameter Distribution ◽  
Sintered Steel ◽  
Weibull Statistics ◽  
Sintered Steels ◽  
Anderson Darling ◽  
Two Parameter

Abstract A statistical analysis is presented of tensile and bending strengths of a porous sintered structural steel which exhibits non-linear, quasi-brittle, behaviour. It is the result of existing natural flaws (pores and oxide inclusions) and of the formation of fresh flaws when stress is applied. The analysis is by two- and three-parameter Weibull statistics. Weibull modulus, a measure of reliability, was estimated by the maximum likelihood method for specimen populations < 30. Probability distributions were compared on the basis of goodness to fit using the Anderson-Darling tests. The use of the two-parameter Weibull distribution for strength data of quasi-brittle sintered steels is questioned, because there is sufficient evidence that the 3-parameter distribution fits the data better.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

scholarly journals Moment based Estimation for the Shape Parameters, Effect it on Some Probability Statistical Distributions Using the Moment Method and Maximum Likelihood Method

2020 ◽  
Vol 5 (6) ◽  
pp. 979-986
Author(s):  
Hassan Tawakol A. Fadol
Keyword(s):  
Maximum Likelihood ◽  
Shape Parameter ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Estimation Method ◽  
Simulation Method ◽  
Likelihood Method ◽  
Inductive Method ◽  
Binomial Distributions ◽  
Best Estimate

The purpose of this paper was to identify the values of the parameters of the shape of the binomial, bias one and natural distributions. Using the estimation method and maximum likelihood Method, the criterion of differentiation was used to estimate the shape parameter between the probability distributions and to arrive at the best estimate of the parameter of the shape when the sample sizes are small, medium, The problem was to find the best estimate of the characteristics of the society to be estimated so that they are close to the estimated average of the mean error squares and also the effect of the estimation method on estimating the shape parameter of the distributions at the sizes of different samples In the values of the different shape parameter, the descriptive and inductive method was selected in the analysis of the data by generating 1000 random numbers of different sizes using the simulation method through the MATLAB program. A number of results were reached, 10) to estimate the small shape parameter (0.3) for binomial distributions and Poisson and natural and they can use the Poisson distribution because it is the best among the distributions, and to estimate the parameter of figure (0.5), (0.7), (0.9) Because it is better for binomial binomial distributions, when the size of a sample (70) for a teacher estimate The small figure (0.3) of the binomial and boson distributions and natural distributions can be used for normal distribution because it is the best among the distributions.

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

scholarly journals The Weibull-Gamma Distribution: Properties and Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 438 ◽  
Author(s):  
Hadeel S. Klakattawi
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Maximum Likelihood Method ◽  
Data Distribution ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Great Flexibility ◽  
Special Cases ◽  
New Distribution ◽  
Family Of Distributions

A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

scholarly journals The Exponentiated Generalized Standardized Half-logistic Distribution

2017 ◽  
Vol 6 (3) ◽  
pp. 24 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Thiago A. N. De Andrade ◽  
Marcelo Bourguignon ◽  
Frank Gomes-Silva
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Data Set ◽  
Lorenz Curves ◽  
Lifetime Model ◽  
Two Parameter ◽  
New Distribution

We study a new two-parameter lifetime model called the exponentiated generalized standardized half-logistic distribution, which extends the half-logistic pioneered by Balakrishnan in the eighties. We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, and order statistics. The model parameters are estimated by the maximum likelihood method. A simulation study reveals that the estimators have desirable properties such as small biases and variances even in moderate sample sizes. We prove empirically that the new distribution provides a better fit to a real data set than other competitive models.

scholarly journals Seasonal variation in the trawl codend selectivity of picarel (Spicare smaris)

2007 ◽  
Vol 64 (8) ◽  
pp. 1569-1572 ◽  
Author(s):  
Hüseyin Özbilgin ◽  
Zafer Tosunoğlu ◽  
Adnan Tokaç ◽  
Gülnur Metin
Keyword(s):  
Seasonal Variation ◽  
Maximum Likelihood ◽  
Water Temperature ◽  
Maximum Likelihood Method ◽  
Aegean Sea ◽  
Logistic Equation ◽  
Likelihood Method ◽  
Sufficient Evidence ◽  
Marine Science ◽  
Summer Feeding

Abstract Özbilgin, H., Tosunoğlu, Z., Tokaç, A., and Metin, G. 2007. Seasonal variation in the trawl codend selectivity of picarel (Spicare smaris). – ICES Journal of Marine Science, 64: 1569–1572. Seasonal selectivity of commercial 40 mm polyethylene codend was tested for picarel (Spicara smaris) in spring (4–18 April 2002), summer (10–25 July 2002), autumn (26 September–2 October 2002), and winter (22–23 January 2003) in the Aegean Sea. Data were collected using the covered codend technique and analysed using the logistic equation with the maximum likelihood method. Four sets of selection curves were analysed and compared using the model developed by Fryer (1991). Highest L50 is in autumn (13.82 cm; s.e. 0.62), when water temperature is highest and the fish are expected to be in their best condition after summer feeding. Lowest L50 is in spring (11.09 cm; s.e. 0.51), when water temperature is lowest and the fish are at their spawning stage. However, there is not sufficient evidence to say that the seasonal variation in the selectivity of 40 mm polyethylene codend for picarel is statistically significant (p > 0.05).

scholarly journals A New Family of Continuous Probability Distributions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 194
Author(s):  
M. El-Morshedy ◽  
Fahad Sameer Alshammari ◽  
Yasser S. Hamed ◽  
Mohammed S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Method ◽  
Model Parameters ◽  
Finite Sample ◽  
Graphical Simulation ◽  
New Family ◽  
The One

In this paper, a new parametric compound G family of continuous probability distributions called the Poisson generalized exponential G (PGEG) family is derived and studied. Relevant mathematical properties are derived. Some new bivariate G families using the theorems of “Farlie-Gumbel-Morgenstern copula”, “the modified Farlie-Gumbel-Morgenstern copula”, “the Clayton copula”, and “the Renyi’s entropy copula” are presented. Many special members are derived, and a special attention is devoted to the exponential and the one parameter Pareto type II model. The maximum likelihood method is used to estimate the model parameters. A graphical simulation is performed to assess the finite sample behavior of the estimators of the maximum likelihood method. Two real-life data applications are proposed to illustrate the importance of the new family.

scholarly journals A New Extension of Lindley Geometric Distribution and its Applications

2019 ◽  
pp. 249-263
Author(s):  
I. Elbatal ◽  
Mohamed G. Khalil
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Geometric Distribution ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Distribution

A new four-parameter distribution called the beta Lindley-geometric distribution is proposed. The hazard rate function of the new model can be constant, decreasing, increasing, upside down bathtub or bathtub failure rate shapes. Various structural properties including of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated using a real data set.

scholarly journals The Topp-Leone Generated Weibull Distribution: Regression Model, Characterizations and Applications

2016 ◽  
Vol 6 (1) ◽  
pp. 126 ◽  
Author(s):  
Gokarna R. Aryal ◽  
Edwin M. Ortega ◽  
G. G. Hamedani ◽  
Haitham M. Yousof
Keyword(s):  
Weibull Distribution ◽  
Regression Model ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Lifetime Model ◽  
First Time ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new four-parameter lifetime model called the Topp Leone Generated Weibull (TLGW) distribution. This distribution is a generalization of the two parameter Weibull distribution using the genesis of Topp-Leone distribution.  We derive many of its structural properties including ordinary and incomplete moments, quantile and generating functions and order statistics. Parameter estimation using maximum likelihood method and simulation results to assess effectiveness of the distribution are discussed. Also, for the first time, we introduce a regression model based on the new distribution. We prove empirically the importance and flexibility of the new model in modeling various types of real data sets.

scholarly journals Information Geometry of Randomized Quantum State Tomography

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 609
Author(s):  
Akio Fujiwara ◽  
Koichi Yamagata
Keyword(s):  
Quantum State ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Information Geometry ◽  
Likelihood Method ◽  
Mutually Unbiased Bases ◽  
Quantum State Tomography ◽  
Unknown Quantum State ◽  
State Tomography ◽  
Insight Into

Suppose that a d-dimensional Hilbert space H ≃ C d admits a full set of mutually unbiased bases | 1 ( a ) 〉 , ⋯ , | d ( a ) 〉 , where a = 1 , ⋯ , d + 1 . A randomized quantum state tomography is a scheme for estimating an unknown quantum state on H through iterative applications of measurements M ( a ) = | 1 ( a ) 〉 〈 1 ( a ) | , ⋯ , | d ( a ) 〉 〈 d ( a ) | for a = 1 , ⋯ , d + 1 , where the numbers of applications of these measurements are random variables. We show that the space of the resulting probability distributions enjoys a mutually orthogonal dualistic foliation structure, which provides us with a simple geometrical insight into the maximum likelihood method for the quantum state tomography.

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