Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obtained as the discrete counterparts of either the distribution function or the failure rate function of the standard Weibull model. Which lead to different models. This paper discusses the discrete model which is the counterpart of the standard two-parameter Weibull distribution. It covers the determination of the probability mass function, cumulative distribution function, survivor function, hazard function, and the pseudo-hazard function.
This paper is concerned with preliminary test double stage shrinkage estimators to estimate the variance (s2) of normal distribution when a prior estimate of the actual value (s2) is a available when the mean is unknown , using specifying shrinkage weight factors y(×) in addition to pre-test region (R).
Expressions for the Bias, Mean squared error [MSE (×)], Relative Efficiency [R.EFF (×)], Expected sample size [E(n/s2)] and percentage of overall sample saved of proposed estimator were derived. Numerical results (using MathCAD program) and conclusions are drawn about selection of different constants including in the me
... Show MoreIn this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and the hazard function are found. The behaviour of probability density function for MWPDTI distrib
... Show MoreIn this research work an attempt has been made to investigate about the Robustness of the Bayesian Information criterion to estimate the order of the autoregressive process when the error of this model, Submits to a specific distributions and different cases of the time series on various size of samples by using the simulation, This criterion has been studied by depending on ten distributions, they are (Normal, log-Normal, continues uniform, Gamma , Exponential, Gamble, Cauchy, Poisson, Binomial, Discrete uniform) distributions, and then it has been reached to many collection and recommendations related to this object , when the series residual variable is subject to each ( Poisson , Binomial , Exponential , Dis
... Show MoreIn this paper, Bayes estimators of the parameter of Maxwell distribution have been derived along with maximum likelihood estimator. The non-informative priors; Jeffreys and the extension of Jeffreys prior information has been considered under two different loss functions, the squared error loss function and the modified squared error loss function for comparison purpose. A simulation study has been developed in order to gain an insight into the performance on small, moderate and large samples. The performance of these estimators has been explored numerically under different conditions. The efficiency for the estimators was compared according to the mean square error MSE. The results of comparison by MSE show that the efficiency of Bayes est
... Show MoreThe fingerprints are the more utilized biometric feature for person identification and verification. The fingerprint is easy to understand compare to another existing biometric type such as voice, face. It is capable to create a very high recognition rate for human recognition. In this paper the geometric rotation transform is applied on fingerprint image to obtain a new level of features to represent the finger characteristics and to use for personal identification; the local features are used for their ability to reflect the statistical behavior of fingerprint variation at fingerprint image. The proposed fingerprint system contains three main stages, they are: (i) preprocessing, (ii) feature extraction, and (iii) matching. The preprocessi
... Show MoreThis paper deals with the mathematical method for extracting the Exponential Rayleighh distribution based on mixed between the cumulative distribution function of Exponential distribution and the cumulative distribution function of Rayleigh distribution using an application (maximum), as well as derived different statistical properties for distribution, and present a structure of a new distribution based on a modified weighted version of Azzalini’s (1985) named Modified Weighted Exponential Rayleigh distribution such that this new distribution is generalization of the distribution and provide some special models of the distribution, as well as derived different statistical properties for distribution
Improving speaking skills of Iraqi EFL students was the main purpose of the current research. Thirty EFL students were selected as the research participants for achieving this aim. All students completed the pretest and then spent the next 25 weeks meeting for 90 minutes each to present their nine lectures, answer difficult questions, and get feedback on their use of language in context. Progressive-tests, posttests and delayed post-tests followed every three courses. The researcher utilized SPSS 22 to anal Analyze the data descriptively and inferentially after doing an ANOVA on repeated measurements. It has been shown that using the ideas of sociocultural theory in the classroom has an important and positive impact on students of
... Show MoreHigh performance self-consolidating concrete HP-SCC is one of the most complex types of concrete which have the capacity to consolidated under its own weight, have excellent homogeneity and high durability. This study aims to focus on the possibility of using industrial by-products like Silica fumes SF in the preparation of HP-SCC enhanced with discrete steel fibers (DSF) and monofilament polypropylene fibers (PPF). From experimental results, it was found that using DSF with volume fraction of 0.50 %; a highly improvements were gained in the mechanical properties of HP-SCC. The compressive strength, splitting tensile strength, flexural strength and elastic modulus improved about 65.7 %, 70.5 %, 41.7 % and 80.3 % at 28 days age, respectively
... Show MoreThe cost of pile foundations is part of the super structure cost, and it became necessary to reduce this cost by studying the pile types then decision-making in the selection of the optimal pile type in terms of cost and time of production and quality .So The main objective of this study is to solve the time–cost–quality trade-off (TCQT) problem by finding an optimal pile type with the target of "minimizing" cost and time while "maximizing" quality. There are many types In the world of piles but in this paper, the researcher proposed five pile types, one of them is not a traditional, and developed a model for the problem and then employed particle swarm optimization (PSO) algorithm, as one of evolutionary algorithms with t
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