Parameters Of Exponential Distribution Research Articles

Pitman closeness of predictors of future order statistics for two parameter exponential distribution

In this paper, the Pitman closeness of predictors for a future order statistic coming from a two parameter exponential distribution is discussed. The optimum equivariant predictor using the Pitman closeness criterion is derived and compared with the best invariant predictor and the best unbiased predictor. The predictors are obtained on the basis of observed record values. Exact expressions for the required Pitman closeness probabilities are derived when both parameters are considered to be unknown. Similar results are obtained for the predictors of the mean of a future sample from exponential distribution. Several tables which contain numerical computations, are provided in order to compare the predictors in the sense of Pitman's measure of closeness.

Estimation under failure-censored step-stress life test for the generalized exponential distribution parameters

Accelerated life testing of materials is used to collect failure data quickly when the lifetime of a specimen under use condition is too long. This article considers estimates of the generalized exponential distribution parameters under step-stress partially accelerated life testing with Type-II censoring. The maximum likelihood approach is applied to derive point and asymptotic confidence interval estimations of the model parameters. The performance of the estimators is evaluated numerically for different parameter values and different sample sizes via their mean square error. Also, the average confidence intervals lengths and the associated coverage probabilities are obtained. A simulation study is conducted for illustration.

Product Spacings as an Alternative to Likelihood for Bayesian Inferences

The paper aims to study the consequences of using product of spacings (PS) as an alternative to the traditional likelihood under Bayesian set up. For this purpose we have considered the problem of point estimation of the parameter of exponential distribution. We have also obtained the asymptotic and HPD confidence intervals of the parameter. The proposed estimates have been compared with those based on usual likelihood on the basis of simulated samples from exponential distribution.

English

In this study we have some estimators for exponential distribution in simulation study. These estimators were classical estimator like maximum likelihood estimator (MLE) and robust estimators that is called MAD/MED robust estimator. These methods are used to estimate the parameter of exponential distribution  . We applied the simulation in MATLAB and then compared the results that we have them. The results of the study proved that the method of MAD/MED robust is better than the classical method MSE in the event that the data regular (without pollution) or contaminated.

Modeling of fog droplet size distributions from infrared light attenuation measurements

ABSTRACTIt is demonstrated that optical attenuations recorded at 1‐min time interval in foggy environments can be modeled using two parameters of exponential distribution (hereafter EDSD) that are retrieved by standard iterative procedure. To compute two parameters of the exponential distribution, two experimental measurements are required (e.g. the measurement of liquid water content and the optical attenuations at visible wavelength) that are treated as two linear equations. A performance analysis suggests that the newly computed EDSD parameters having average values of Λ = 5.9815, N0 = 6.0586 are well correlated with the infrared light extinction coefficients and show somewhat better agreement with the calculated attenuations. Copyright © 2014 John Wiley & Sons, Ltd.

Minimax Estimation of the Parameter of Exponential Distribution based on Record Values

Bayes estimators of the parameter of exponential distribution are obtained with non- informative quasi-prior distribution based on record values under three loss functions. These functions are weighted squared error loss, square log error loss and entropy loss functions. Finally the minimax estimators of the parameter are obtained by using Lehmann's theorem. Comparisons in terms of risks with the estimators of parameter under three loss functions are also studied.

Erratum to: Estimating the Generalized Exponential Distribution Parameters and the Acceleration Factor under Constant-Stress Partially Accelerated Life Testing with Type-II Censoring

Erratum to: Estimating the Generalized Exponential Distribution Parameters and the Acceleration Factor under Constant-Stress Partially Accelerated Life Testing with Type-II Censoring

Bayes Estimation of Parameter of Exponential Distribution under a Bounded Loss Function

The aim of this study is to study the Bayes estimation of parameter of exponential distribution under a bounded loss function, named reflected gamma loss function, which proposed by Towhidi and Behboodian (1999). The inverse Gamma prior distribution is used as the prior distribution of the parameter of exponential distribution. Bayesian estimators are obtained under squared error loss and the reflected gamma loss functions. Minimum risk equivariant estimator of the parameter is also derived. Finally, a numerical simulation is used to compare the estimators obtained.

Evaluating alternative Frequentist inferential approaches for optimal order quantities in the newsvendor model under Exponential demand

Three estimation policies for the optimal order quantity of the classical newsvendor model under exponential demand are evaluated in the current paper. According to the principle of the first estimation policy, the corresponding estimator is obtained replacing in the theoretical formula which gives the optimal order quantity the parameter of exponential distribution with its maximum likelihood estimator. The estimator of the second estimation policy is derived in such a way as to ensure that the requested critical fractile is attained. For the third estimation policy, the corresponding estimator is obtained maximizing the a-priori expected profit with respect to a constant which has been included into the form of the estimator. Three statistical measures have been chosen to perform the evaluation. The actual critical fractile attained by each estimator, the mean square error, and the range of deviation of estimates from the optimal order quantity, when the probability to take such a range is the same for the three estimation policies. The behavior of the three statistical measures is explored under different combinations of sample sizes and critical fractiles. With small sample sizes, no estimation policy predominates over the others. The estimator which attains the closest actual critical fractile to the requested one, this estimator has the largest mean square and the largest range of deviation of estimates from the optimal order quantity. On the contrary, with samples over 40 observations, the choice is restricted among the estimators of the first and third estimation policy. To facilitate this choice, at different sample sizes, we offer the required values of the critical fractile which determine which estimation policy eventually should be applied.

Default Bayesian testing for the scale parameters in two parameter exponential distributions

Abstract In this paper, we consider the problem of testing the equality of the scale parametersin two parameter exponential distributions. We propose Bayesian testing proceduresfor the equality of the scale parameters under the noninformative priors. The nonin-formative prior is usually improper which yields a calibration problem that makes theBayes factor to be de ned up to a multiplicative constant. Thus, we propose the defaultBayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayesfactors under the reference priors. Simulation study and an example are provided.Keywords: Fractional Bayes factor, intrinsic Bayes factor, reference prior, scale param-eter, two parameter exponential distribution. 1. Introduction The exponential distribution plays an important role in the eld of life testing and reliabil-ity. One is referred to Zelen (1966), Johnson and Kotz (1970), Bain (1978) and Lawless andSinghal (1980). The probability density function of two parameter exponential distributionE(;˙) with the location parameter and the scale parameter ˙is given byf(xj;˙) =1˙expˆx ˙˙;x>0;˙>0: (1.1)The decision theoretic estimation of the scale parameter was rstly studied by Arnold(1970). Zidek (1973), Brewster (1974), Kubokawa (1994) and Petropoulos and Kourouklis(2002) considered Bayesian estimation of scale parameter based on decision theory. Also,the estimator of the ratio of the scale parameters from the decision theoretic point of viewwas studied by Madi and Tsui (1990), Madi (2008) and Bobotas and Kourouklis (2011). Allthe papers mentioned above were focused on Bayesian point estimation.

Interval Konfidensi untuk Satu Parameter Distribusi Eksponensial di Bawah Sensor Lengkap dengan Metode Bootstrap (Studi Kasus Data Waktu Tunggu Bencana Gempa Bumi di Bulan Maret 2013)

In this research will be discussed on an interval estimate for the one parameter exponential distribution under complete censored data with a case study of data waiting time for earthquake disaster in March 2013. The exponential distribution has immensely contributed in the analysis of lifetime. Historically the exponential distribution was the first lifetime model in which statistical methods in survival analysis were extensively developed. For samples that are singly failure-censored on the complete censored, confidence intervals on one parameter exponential distribution are obtained from the exact sampling distribution on the following quantity related to the total time on test T.

A hybrid ant colony-computer simulation approach for optimum planning and control of maritime traffic

Ant colony optimisation (ACO) is a meta-heuristic approach to tackle hard combinatorial optimisation problems which has been used to solve several optimisation problems in various fields of engineering. Its basic component is a probabilistic solution construction mechanism. Discrete event simulation (DES) is a method which is used to model real world systems capable of being decomposed into a set of logically separate processes autonomously progressing through time. Each event occurs at an instant of time and indicates a change of state in the system. In this paper, we present the application of ant colony optimisation (ACO) model in discrete event simulation of marine traffic. We use this methodology to compare different distribution functions and to find the best distribution with its associated parameters. We experimentally show that exponential distribution has the best results for creating the simulation events of maritime traffic in Arvand river, Iran. Also, the integrated ACO-DES finds the best exponential distribution parameters for arrival (planning and control) of different kinds of ships in one of the most hazardous, crowded, and potentially dangerous rivers in the world. This is the first study that integrates ACO with DES for identification and optimisation of maritime traffic.

Inference in the generalized exponential distribution under partially accelerated tests with progressive Type-II censoring

Accelerated life testing (ALT) or partially accelerated life testing (PALT) is frequently used in modern reliability engineering. This paper considers the statistical inference on the generalized exponential distribution parameters in presence of progressive Type-II censoring with random removals under PALT, where the number of units removed at each failure time has a binomial distribution. The maximum likelihood method is used to estimate the unknown parameters in the case of step-stress partially accelerated life tests. The performance of the estimators is investigated numerically for different parameter values and sample sizes. Also, the approximate confidence bounds of the model parameters are obtained. Finally, a simulation study is made for illustrative purposes.

An EM Algorithm for Estimating the Parameters of the Generalized Exponential Distribution under Unified Hybrid Censored Data

The unified hybrid censoring is a mixture of generalized Type-I and Type-II hybrid censoring schemes. This article presents the statistical in- ferences on Generalized Exponential Distribution parameters when the data are obtained from the unified hybrid censoring scheme. It is observed that the maximum likelihood estimators can not be derived in closed form. The EM algorithm for computing the maximum likelihood estimators is proposed. We calculated the observed Fisher information matrix using the missing infor- mation principle which is useful for constructing the asymptotic confidence intervals. Simulations studies are performed to compare the performances of the estimators obtained under different schemes. Finally, a real data set has been analyzed for illustrative purposes.

Effect of the Seasonal Rainfall Distribution on Storm-Water Quality Capture Volume Estimation

Thewater quality capturevolume (WQCV) is a design parameter that is used for sizing urban storm-water treatment facilities. The storage, treatment, overflow, and runoff model (STORM) in NetSTORM was used to translate historical hourly rainfall records into storm event runoff data and to compute the WQCV (set at the 85th percentile capture of the annual runoff volume) of eight cities located in various climatological areas of South Korea. For each city, one-parameter and two-parameter exponential distributions were fitted to the set of storm event runoff volumes that were computed by STORM, and the 85th percentile runoff volume that was determined from the STORM was compared to the 85th percentile runoff volumes that were obtained from the two exponential distributions. The results demonstrate that the more easily applied distribution approach is adequate in South Korea for determining the WQCV. In Seoul, which is a city located in the northwestern part of South Korea, the two-parameter exponential distribution yielded the best estimate of the WQCV computed by STORM. For Chuncheon, Wonju, and Daejeon, which are cities located in the north-central and central parts of South Korea, the WQCVs were accurately estimated using both the one-parameter and two-parameter exponential distributions. Finally, in the cities of Gangneung, Gwangju, Daegu, and Busan, which are located in the northeastern and southern parts of South Korea, the WQCVs were best estimated using the one- parameter exponential distribution. It was found that seasonal variations in rainfall and rainfall event depth are important factors in assessing the WQCV. This study also found that the one-parameter exponential distribution approach, which is the most common approach used in the United States, may not be adequate for WQCVestimation if the standard deviation for average monthly rainfall is significant. DOI: 10.1061/ (ASCE)WR.1943-5452.0000204. © 2013 American Society of Civil Engineers. CE Database subject headings: Nonpoint pollution; Parameters; Rainfall; Seasonal variations; South Korea; Stormwater management; Water quality.

ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS

The exponential distribution is commonly used to model the behavior of units that have a constant failure rate. The two-parameter exponential distribution provides a simple but nevertheless useful model for the analysis of lifetimes, especially when investigating reliability of technical equipment.This paper is concerned with estimation of parameters of the two parameter (location and scale) exponential distribution. We used the least squares method (LSM), relative least squares method (RELS), ridge regression method (RR),  moment estimators (ME), modified moment estimators (MME), maximum likelihood estimators (MLE) and modified maximum likelihood estimators (MMLE). We used the mean square error MSE, and total deviation TD, as measurement for the comparison between these methods. We determined the best method for estimation using different values for the parameters and different sample sizes

Statistical Inference of LZL-Type Mass Flowmeter Life Distribution Model

Characteristics of field failure data are analyzed in this paper. The failure data and sales record of LZL-type mass flowmeter are used to infer life distribution of this conduct. The lines can be fitted in coordinates of six distribution using least square and the residual sum of squares are compared, the minimum correspond is the best distribution type. The results show that the life distribution style of this conduct is the two parameter exponential distribution, which is the base to analyze and predict failure development, research failure mechanism and draw up maintenance policy.

Estimating reliability parameters under insufficient information

The paper presents an algorithm to search for the lower bound of the Bayesian estimate of the parameter of exponential distribution in the case where it is known that a priori distribution belongs to the class of all distribution functions with two equal quantiles. This problem arises in sensivity analysis of Bayesian estimates of failure rates to the choice of a priori distribution in the exponential failure model.

On Robustness of a Sequential Test for Scale Parameter of Gamma and Exponential Distributions

The main aim of the present paper is to study the robustness of the developed sequential probability ratio test (SPRT) for testing the hypothesis about scale parameter of gamma distribution with known shape parameter and exponential distribution with location parameter. The robustness of the SPRT for scale parameter of gamma distribution is studied when the shape parameter has undergone a change. The similar study is conducted for the scale parameter of exponential distribution when the location parameter has undergone a change. The expressions for operating characteristic and average sample number functions are derived. It is found in both the cases that the SPRT is robust only when there is a slight variation in the shape and location parameter in the respective distributions.

Improved Classes of Scale Parameter towards an Interval of Exponential Distribution

Abstract In this paper we envisaged some improved classes of shrinkage estimators for estimating scale parameter of one parameter exponential distribution, when some apriori or guessed interval containing the parameter θ (say) is available from some past experiences. Simulation study have carried out to verify the high efficiency of the proposed new classes of estimators when compared with the usual consistent estimators, unbiased estimator, minimum mean squared error estimator and Singh and Chander's estimators.