New Bayes Estimator of Parameter Weibull Distribution

Alkutubi, Hadeel Salim; AlShemmary, Ebtesam N.; Yasseen, Shaymaa abed; Alwan, Yasser H.

doi:10.14419/ijbas.v1i3.113

Cited by 3 publications

(4 citation statements)

References 4 publications

(4 reference statements)

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“…By applying the ordinary least squares method (OLS), which makes the sum of the squares of errors as small as possible, by performing partial differential with respect to the parameters (𝑏 2 ̂, 𝑏 1 ̂, 𝑎 ̂) after setting them equal to zero, we obtained the following equations: [4], [5] ∑ From the equation (3), we get: 6) Therefore, the parameter 𝑎 ̂ can be obtained from equation (6), as follows:…”

Section: Multiple Regressions Modelmentioning

confidence: 99%

Using Regression Model to Study the Significant Differences in the Number of Covid-19 Infections

Murad,

Alkutubi,

Al Shamary

2024

Jour. Kufa Math. Comp.

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Multiple linear regression modeling was used to analyze Covid-19 data, which represents the number of infections in Iraq for the year 2019, in order to find occupational discrepancies between the dependent variable (age) and the independent factors under discussion. This was carried out in addition to the correlation value. Following statistical analysis, a significant correlation was discovered between the independent factors and the dependent variable, age. The age dependent variable and the research's independent variables are evidently different from one another in a substantial degree, as indicated by the analysis of variance table. This is in addition to comparing the number of infections between boys and females for each of the study's variables (blood pressure, oxygen rate, sugar rate, and D-Dimer), and we discovered that there are no appreciable variations in the quantity of infections between males and females based on the factorial experiment analysis.

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Section: Multiple Regressions Modelmentioning

confidence: 99%

Using Regression Model to Study the Significant Differences in the Number of Covid-19 Infections

Murad,

Alkutubi,

Al Shamary

2024

Jour. Kufa Math. Comp.

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“…Zhang et al 17 assumed b as known and just used the conjugate gamma prior for a for Bayesian life test planning. Nevertheless, the continuous-discrete prior model has been often criticized because of the difficulty of specifying an appropriate categorical prior for b. Sinha 18 found the Weibull Jeffrey's prior to be f(a,b) ∝ (ab) À 1 , which has often been applied in an extended form for Bayesian estimation of just one or both Weibull parameters, see, for example, Guure et al, 19 Pandey et al, 20 Ahmed et al, 21 Ahmed et al 22 or Alkutubi et al 23 Further ideas on non-informative priors for the Weibull distribution are provided by Sun, 24 whereas Kundu 25 presented an informative prior for censored Weibull lifetime data employing independent gamma and log-concave priors for a and b, respectively. However, all of these approaches have just been extended to (censored) time-to-failure data.…”

Section: Glossary: a Bmentioning

confidence: 99%

“…Sinha found the Weibull Jeffrey's prior to be f ( a , b ) ∝ ( ab ) − 1 , which has often been applied in an extended form for Bayesian estimation of just one or both Weibull parameters, see, for example, Guure et al ., Pandey et al ., Ahmed et al ., Ahmed et al . or Alkutubi et al . Further ideas on non‐informative priors for the Weibull distribution are provided by Sun, whereas Kundu presented an informative prior for censored Weibull lifetime data employing independent gamma and log‐concave priors for a and b , respectively.…”

Section: Introductionmentioning

confidence: 99%

Advanced Bayesian Estimation of Weibull Early Life Failure Distributions

Kurz

Lewitschnig

Pilz

2014

Quality & Reliability Eng

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In semiconductor manufacturing, it is a key to ensure reliability of the produced devices. The population's reliability level is demonstrated by means of a burn‐in study (that is investigating a large number of devices under real‐life stress conditions for product relevant fails). Burn‐in settings are based on the lifetime distribution of early fails. Typically, it is modelled as a Weibull distribution Wb(a,b) with scale parameter a > 0 and shape parameter b ∈ (0,1) motivated by a decreasing failure rate within the devices' early life. Depending on the applied burn‐in scheme, the Weibull parameters have to be estimated from time‐to‐failure and discrete failure count data, respectively. In this paper, we present advanced Bayesian estimation models for the Weibull distribution handling both data situations. First, a simplified conjugate approach using gamma‐histogram‐beta priors is presented. Further, according to the paper's main focus, an extended Bayesian concept for assessing Weibull early life failure distributions is highlighted. It is characterized by a Dirichlet prior distribution applied to the lifetime function of early fails. The proposed model simplifies the incorporation of engineering prior knowledge. Moreover, it can be extended to both discrete failure and time‐to‐failure burn‐in data. The joint posterior distribution, Bayesian estimators and compounded and joint credible regions are derived by means of Monte Carlo simulation. The principle of Bayesian learning allows to update the Weibull early life failure distribution whenever new failure data become available. Therefore, burn‐in settings can dynamically be adapted improving the efficiency of burn‐in. Copyright © 2014 John Wiley & Sons, Ltd.

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“…While there are major differences among classical methods, Bayesian methods basically use the same formulation, as will be discussed later; they differ only by the choice of the prior distribution of the parameters [17,18]. In the general scientific literature, there are many Bayesian point estimation studies on , see for example [42][43][44][45][46][47]; however Bayesian interval estimation studies are limited, see Aron et al [48] as an example. The details of Bayesian Weibull analysis can be found in [49].…”

Section: Introductionmentioning

confidence: 99%