Bootstrap Intervals of the Parameters of Lognormal Distribution Using Power Rule Model and Accelerated Life Tests

Assumed that the distribution of the lifetime of any unit follows a lognormal distribution with parameters μ and σ . Also, assume that the relationship between μ and the stress level V is given by the power rule model. Several types of bootstrap intervals of the parameters were studied and their performance was studied using simulations and compared in term of attainment of the nominal confidence level, symmetry of lower and upper error rates and the expected width. Conclusions and recommendations are given

Estimating the Parameters of Rayleigh Cumulative Exposure Model in Simple Step-Stress Testing. Natasha Beretvas is an

Assumes the life distribution of a test unit for any stress follows a Rayleigh distribution with scale parameterθ , and that Ln(θ ) is a linear function of the stress level. Maximum likelihood estimators of the parameters under a cumulative exposure model are obtained. The approximate variance estimates obtained from the asymptotic normal distribution of the maximum likelihood estimators are used to construct confidence intervals for the model parameters. A simulation study was conducted to study the performance of the estimators. Simulation results showed that in terms of bias, mean squared error, attainment of the nominal confidence level, symmetry of lower and upper error rates and the expected interval width, the estimators are very accurate and have a high level of precision

Comparison Of Some Simple Estimators Of The Lognormal Parameters Based On Censored Samples

Point estimation of the parameters of the lognormal distribution with censored data is considered. The often employed maximum likelihood estimator does not exist in closed form and iterative methods that require very good starting points are needed. In this article, some techniques of finding closed form estimators to this situation are presented and extended. An extensive simulation study is carried out to investigate and compare the performance of these techniques. The results show that some of them are highly efficient as compared with the maximum likelihood estimator

Estimating The Slope Of Simple Linear Regression In The Presence Of Outliers

In this article, an estimation procedure to simple linear regression in the presence of outliers is proposed. The performance of the proposed estimator, the AM estimator, is compared with other traditional estimators: least squares, Theil type repeated median, and geometric mean. A numerical example is given to illustrate the proposed estimator. Simulation results indicate that the proposed estimator is accurate and has a high precision in the presence of outliers

The predictors to medication adherence among adults with diabetes in the United Arab Emirates.

BackgroundDiabetes is a chronic medical condition and adherence to medication in adults with diabetes is important. Identifying predictors to medication adherence in adults with diabetes would help identify vulnerable patients who are likely to benefit by improving their adherence levels.MethodsWe conducted a cross-sectional study at the Dubai Police Health Centre between February 2015 and November 2015. Questionnaires were used to collect socio-demographic, clinical and disease related variables and the primary measure of outcome was adherence levels as measured by the Morisky Medication Adherence Scale (MMAS-8©). Multivariate logistic regression was carried out to identify predictors to adherence.ResultsFour hundred and forty six patients were interviewed. Mean age 61 year +/- 11. 48.4 % were male. The mean time since diagnosis of diabetes was 3.2 years (Range 1-15 years). Two hundred and eighty eight (64.6 %) patients were considered non-adherent (MMAS-8© adherence score < 6) while 118 (26.5 %) had moderate adherence (MMAS-8© adherence score 6 = <8) and 40 (9.0 %) high adherence (MMAS-8© adherence scores <8) to their medication respectively. The strongest predictor for adherence as predicted by the multi-logistic regression model was the patient's level of education. A technical diploma certificate as compared to a primary school level of education was the strongest predictor of adherence (OR = 66.1 CI: 6.93 to 630.43); p < 0.001). The patient's age was also a predictor of adherence with older patients reporting higher levels of adherence (OR = 1.113 (CI: 1.045 to 1.185; p = 0.001 for every year increase in age). The duration of diabetes was also a predictor of adherence (OR = 1.830 (CI: 1.270 to 2.636; p = 0.001 for every year increase in the duration of diabetes). Other predictors to medication adherence include Insulin use, ethnicity and certain cultural behaviours.ConclusionA number of important predictors to medication adherence in diabetics were identified in this study. Such predictors could help develop policies for improving adherence in diabetics

The effect of cement type on the potential and corrosion behaviour of steel reinforcement

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Semi-Parametric Method to Estimate the Time-to-Failure Distribution and its Percentiles for Simple Linear Degradation Model

Most reliability studies obtained reliability information by using degradation measurements over time, which contains useful data about the product reliability. Parametric methods like the maximum likelihood (ML) estimator and the ordinary least square (OLS) estimator are used widely to estimate the time-to-failure distribution and its percentiles. In this article, we estimate the time-to-failure distribution and its percentiles by using a semi-parametric estimator that assumes the parametric function to have a half- normal distribution or an exponential distribution. The performance of the semi-parametric estimator is compared via simulation study with the ML and OLS estimators by using the mean square error and length of the 95% bootstrap confidence interval as the basis criteria of the comparison. An application to real data is given. In general, if there are assumptions on the random effect parameter, the ML estimator is the best; otherwise the kernel semi- parametric estimator with half-normal distribution is the best

Optimum Times for Step-Stress Cumulative Exposure Model Using Log-Logistic Distribution with Known Scale Parameter

Abstract: In this paper we assume that the life time of a test unit follows a log-logistic distribution with known scale parameter. Tables of optimum times of changing stress level for simple step-stress plans under a cumulative exposure model are obtained by minimizing the asymptotic variance of the maximum likelihood estimator of the model parameters at the design stress with respect to the change time. Zusammenfassung: In diesem Aufsatz wird angenommen, dass die Lebensdauer einer Testeinheit einer log-logistischen Verteilung mit bekanntem Skalenparameter genügt. Tabellen für die optimalen Zeitpunkte eines Wechsels des Belastungsniveaus für einfache step-stress Pläne unter einem kumulativen Expositionsmodells erhält man durch Minimieren der asymptotischen Varianz des Maximum Likelihood Schätzers der Modellparameter zur zulässigen Spannung bezüglich der Wechselzeit

Stylolite in Upper Cretaceous Carbonate Reservoirs from Northwestern Iraq

Stylolites are commonly observed in the carbonate reservoirs in various oilfield of Iraq including those of upper Cretaceous successions from northwestern Iraq, where they are characterized by stylolite-rich zones in the Cenomanian-early Turonian Gir Bir Formation and to a lesser extent in the Turonian-Santonian Wajna and early Campanian Mushorah formations respectively. The observed stylolites are either large to be identified in the core samples or smaller ones that are well observed in the thin sections and are characterized by variations in amplitude, morphology and accumulated insoluble residues. The recorded stylolites are classified as hummocky, irregular, low and high-amplitudes peaks, and irregular anastomosing stylolites. Stylolites affect the porosity permeability and thickness reduction compaction as the main chemical compaction (pressure solution) that reduce porosity. Whereas, in other places, the stylolites act as seals and stop the upward movement of hydrocarbons. This is also seen for mineralization processes such as silicification that ended near the stylolite surfaces

Variable Scale Kernel Density Estimation for Simple Linear Degradation Model

In this study, we proposed the variable scale kernel estimator for analyzing the degradation data. The properties of the proposed method are investigated and compared with the classical method such as; maximum likelihood and ordinary least square methods via simulation technique. The criteria bias and MSE are used for comparison. Simulation results showed that the performance of the variable scale kernel estimator is acceptable as a general estimator. It is nearly the best estimator when the assumption of the distribution is invalid. Application to real data set is also given