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Novel entropy estimators of a continuous random variable

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第2期10卷 95-113页

作者： amer ibrahim al-omari Abdul Haq Department of Mathematics Faculty of Science Al al-Bayt UniversityMafraq25113Jordan†Department of StatisticsQuaid-i-Azam University I slamabad45320Pakistan

This paper presents some novel entropy estimators of a continuous random variable using simple random sampling(SRS),ranked set sampling(RSS),and double RSS(DRSS)*** theoretical results of the proposed entropy estimators are *** proposed entropy estimators are compared in terms of the bias and the root mean squared errors,theoretically and numerically,with the Vasicek O.[A test for normality based on sample entropy,***.B 38:54–59,1976.]entropy estimators using SRS,RSS,and DRSS *** turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.

关键词： Entropy bias root mean-squared error double ranked set sampling ranked set sampling simple random sampling

Inverse Length Biased Maxwell Distribution:Statistical Inference with an Application

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Computer Systems Science & Engineering 2021年第10期39卷 147-164页

作者： amer ibrahim al-omari Ayed R.A.alanzi Department of Mathematics Faculty of ScienceAl al-Bayt UniversityMafraqJordan Department of Mathematics College of Science and Human Studies at Hotat SudairMajmaah UniversityMajmaah 11952Saudi Arabia

In this paper,we suggested and studied the inverse length biased Maxell distribution(ILBMD)as a new continuous distribution of one *** ILBMD is obtained by considering the inverse transformation technique of the Maxwell length biased *** characteristics of the ILBMD such as the moments,moment generating function,mode,quantile function,the coefficient of variation,coefficient of skewness,Moors and Bowley measures of kurtosis and skewness,stochastic ordering,stress-strength reliability,and mean deviations are *** addition,the Bonferroni and Lorenz curves,Gini index,the reliability function,the hazard rate function,the reverse hazard rate function,the odds function,and the distributions of order statistics for the ILBMD,are *** ILBMD parameter is estimated using the maximum likelihood method,the method of moments,the maximum product of spacing technique,the ordinary and weight least square procedures,and the Cramer-Von-Mises *** Fishers information,as well as the Rényi and q-entropies,are *** investigate the usefulness of the proposed lifetime distribution and to illustrate the purpose of the study,a real dataset of the relief times of 20 patients receiving an analgesic is used.

关键词： Maxell distribution inverse length biased Maxwell distribution Fisher’s information methods of estimation goodness of fit tests

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

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Computers, Materials & Continua 2021年第4期67卷 285-301页

作者： amer ibrahim al-omari ibrahim M.almanjahie Olena Kravchuk Department of Mathematics Faculty of ScienceAl al-Bayt UniversityMafraqJordan Department of Mathematics College of ScienceKing Khalid UniversityAbha62529Saudi Arabia Statistical Research and Studies Support Unit King Khalid UniversityAbha62529Saudi Arabia School of Agriculture University of AdelaideAdelaideSA 5000Australia

In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned *** the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are *** addition,the values of the corresponding operating characteristic function and the associated producer’s risks are *** of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an *** are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample *** is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this *** suggested acceptance sampling plans are recommended for practitioners in the field.

关键词： Acceptance sampling plan producer’s risk truncated life tests operating characteristic function length-biased weighted lomax distribution consumer’s risk

The Robust Regression Methods for Estimating of Finite Population Mean Based on SRSWOR in Case of Outliers

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Computers, Materials & Continua 2020年第10期65卷 125-138页

作者： Mir Subzar amer ibrahim al-omari Ayed R.A.alanzi Division of Agricultural Statistics SKUAST-K Shalimar190025India Department of Mathematics Faculty of ScienceAl al-Bayt UniversityMafraq25113Jordan Department of Mathematics College of Science and Human Studies at HotatSudairMajmaah UniversityMajmaah11952Saudi Arabia

The ordinary least square(OLS)method is commonly used in regression *** in the presence of outlier in the data,its results are ***,the robust regression methods have been suggested for a long time as alternatives to the OLS to solve the outliers *** the present study,new ratio type estimators of finite population mean are suggested using simple random sampling without replacement(SRSWOR)utilizing the supplementary information in Bowley’s coefficient of skewness with *** these proposed estimators,we have used the OLS,Huber-M,Mallows GM-estimate,Schweppe GM-estimate,and SIS GM-estimate methods for estimating the population ***,the mean square error(MSE)equations of various estimators are obtained and compared with the OLS *** for skewed distributions as the Gamma distribution support the results,and an application of real data set containing outliers is considered for illustration.

关键词： Efficiency GM-estimates Huber-M ordinary least square ratio type estimators

Quantile Version of Mathai-Haubold Entropy of Order Statistics

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Computer Modeling in Engineering & Sciences 2021年第9期128卷 907-925页

作者： ibrahim M.almanjahie Javid Gani Dar amer ibrahim al-omari Aijaz Mir Department of Mathematics College of ScienceKing Khalid UniversityAbha62529Saudi Arabia Statistical Research and Studies Support Unit King Khalid UniversityAbha62529Saudi Arabia Department of Mathematical Sciences IUSTKashmir192231India Department of Mathematics Faculty of ScienceAl al-Bayt UniversityMafraq25113Jordan Department of Mathematics Govt.Degree College KilamHigher EducationJ&K192231India

Many researchers measure the uncertainty of a random variable using quantile-based entropy *** techniques are useful in engineering applications and have some exceptional characteristics than their distribution function *** order statistics,the key focus of this article is to propose new quantile-based Mathai-Haubold entropy and investigate its *** divergence measure of theMathai-Haubold is also considered and some of its properties are ***,based on order statistics,we propose the residual entropy of the quantile-based Mathai-Haubold and some of its property results are *** performance of the proposed quantile-based Mathai-Haubold entropy is investigated by simulation ***,a real data application is used to compare our proposed quantile-based entropy to the existing quantile *** results reveal the outperformance of our proposed entropy to the other entropies.

关键词： Shannon entropy Mathai-Haubold entropy quantile function residual entropy order statistics failure time reliability measures

Generalized Class of Mean Estimators with Known Measures for Outliers Treatment

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Computer Systems Science & Engineering 2021年第7期38卷 1-15页

作者： ibrahim M.almanjahie amer ibrahim al-omari Emmanuel J.Ekpenyong Mir Subzar Department of Mathematics College of ScienceKing Khalid UniversityAbha62529Saudi Arabia Statistical Research and Studies Support Unit King Khalid UniversityAbha62529Saudi Arabia Department of Mathematics Faculty of ScienceAl al-Bayt UniversityMafraq25113Jordan Department of Statistics Michael Okpara University of AgricultureUmudikeAbiaNigeria Jammu and Kashmir Institute of Mathematical Sciences Srinagar190008India

In estimation theory,the researchers have put their efforts to develop some estimators of population mean which may give more precise results when adopting ordinary least squares(OLS)method or robust regression techniques for estimating regression *** when the correlation is negative and the outliers are presented,the results can be distorted and the OLS-type estimators may give misleading estimates or highly biased ***,this paper mainly focuses on such issues through the use of non-conventional measures of dispersion and a robust estimation ***,we have proposed generalized estimators by using the ancillary information of non-conventional measures of dispersion(Gini’s mean difference,Downton’s method and probabilityweighted moment)using ordinary least squares and then finally adopting the Huber M-estimation technique on the suggested *** proposed estimators are investigated in the presence of outliers in both situations of negative and positive correlation between study and auxiliary *** comparisons and real data application are provided to show the strength of the proposed generalized *** is found that the proposed generalized Huber-M-type estimators are more efficient than the suggested generalized estimators under the OLS estimation method considered in this *** new proposed estimators will be useful in the future for data analysis and making decisions.

关键词： Product estimators ratio estimators regression estimators ordinary least square Huber M mean squared error efficiency

Improved Attribute Chain Sampling Plan for Darna Distribution

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Computer Systems Science & Engineering 2021年第9期38卷 381-392页

作者： Harsh Tripathi amer ibrahim al-omari Mahendra Saha Ayed R.A.alanzi Department of Statistics Central University of RajasthanRajasthanIndia Department of Mathematics Faculty of ScienceAl al-Bayt UniversityMafraqJordan Department of Mathematics College of Science and Human Studies at HotatSudairMajmaah UniversityMajmaah 11952Saudi Arabia

Recently,the Darna distribution has been introduced as a new lifetime *** two-parameter Darna distribution represents is a mixture of two well-known gamma and exponential distributions.A manufacturer or an engineer of products conducts life testing to examine whether the quality level of products meets the customer’s requirements,such as reliability or the minimum *** this article,an attribute modified chain sampling inspection plan based on the time truncated life test is proposed for items whose lifetime follows the Darna *** plan parameters,including the sample size,the acceptance number,and the past lot result of the proposed sampling plan,are determined with the help of the two-point approach considering the acceptable quality level(AQL)and the limiting quality level(LQL).The plan parameters and the corresponding operating characteristic functions of a new plan are provided in tabular form for various Darna distribution ***,a few illustrated examples are presented for various distribution *** usefulness of the proposed attribute modified chain sampling plan is investigated using two real failure time *** results indicate that the proposed sampling plan can reduce the sample size when the termination ratio increases for fixed values of the producer’s risk and acceptance ***,the proposed attribute modified chain sampling inspection plan is recommended to practitioners in the field.

关键词： Attribute chain sampling inspection plan consumer’s risk Darna distribution operating characteristic curve producer’s risk truncated life test

Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked Set Sampling Methods

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Computers, Materials & Continua 2020年第8期64卷 835-857页

作者： amer ibrahim al-omari ibrahim M.almanjahie Amal S.Hassan Heba F.Nagy Department of Mathematics Faculty of ScienceAl al-Bayt UniversityMafraq25113Jordan Department of Mathematics College of ScienceKing Khalid UniversityAbha62529Saudi Arabia Statistical Research and Studies Support Unit King Khalid UniversityAbha62529Saudi Arabia Faculty of Graduate Studies for Statistical Research Cairo UniversityGiza12613Egypt

In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Yalculated under simple random sample,ranked set sampling and median ranked set sampling *** different reliability estimators under median ranked set sampling are *** estimators are obtained when both strength and stress have an odd or an even set *** two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice *** performances of the suggested estimators are compared with their competitors under simple random sample via a simulation *** simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random *** general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample ***:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square *** estimates under ranked set sampling and simple random sample methods.

关键词： Stress-Strength model ranked set sampling median ranked set sampling maximum likelihood estimation mean square error

Stratified Double Quartile Ranked Set Samples

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Journal of Mathematics and System Science 2014年第1期4卷 49-55页

作者： Mahmoud ibrahim Syam Kamarulzaman ibrahim amer ibrahim al-omari] School of Mathematical Sciences University Kebangsaan Malaysia 43600 UKM Bangi Selangor Malaysia al al-Bayt University Faculty of Science Department of Mathematics P.O. Box 130095 Mafraq 25113 Jordan

The procedure of stratified double quartile ranked set sampling （SDQRSS） method is introduced to estimate the population mean. The SDQRSS is compared with the simple random sampling （SRS）, stratified ranked set sampling （SRSS） and stratified simple random sampling （SSRS）. It is shown that SDQRSS estimator is an unbiased of the population mean and more efficient than SRS, SRSS and SSRS for symmetric and asymmetric distributions. In addition, by SDQRSS we can increase the efficiency of mean estimator for specific value of the sample size.

关键词： Ranked set sampling quartile ranked set sampling double quartile ranked set sampling stratified double quartile rankedset sampling.