scholarly journals Extended Exponential Regression Model: Diagnostics and Application to Mineral Data

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2042
Author(s):  
Yolanda M. Gómez ◽  
Diego I. Gallardo ◽  
Jeremias Leão ◽  
Héctor W. Gómez
Keyword(s):  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Exponential Model ◽  
Diagnostic Tools ◽  
Model Diagnostics ◽  
Data Set ◽  
Mineral Data ◽  
The Mean ◽  
Exponential Regression Model ◽  
Positive Line

In this paper, we reparameterized the extended exponential model based on the mean in order to include covariates and facilitate the interpretation of the coefficients. The model is compared with common models defined in the positive line also reparametrized in the mean. Parameter estimation is approached based on the expectation–maximization algorithm. Furthermore, we discuss residuals and influence diagnostic tools. A simulation study for recovered parameters is presented. Finally, an application illustrating the advantages of the model in a real data set is presented.

Model Diagnostics for Bayesian Networks

2006 ◽  
Vol 31 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Sandip Sinharay
Keyword(s):  
Model Checking ◽  
Bayesian Networks ◽  
Real Data ◽  
Diagnostic Tools ◽  
Model Diagnostics ◽  
Posterior Predictive Model Checking ◽  
Item Fit ◽  
Item Functioning ◽  
Data Application ◽  
Educational Assessments

Bayesian networks are frequently used in educational assessments primarily for learning about students’ knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A number of aspects of model fit, those of usual interest to practitioners, are assessed using various diagnostic tools. This article suggests a direct data display for assessing overall fit, suggests several diagnostics for assessing item fit, suggests a graphical approach to examine if the model can explain the association among the items, and suggests a version of the Mantel–Haenszel statistic for assessing differential item functioning. Limited simulation studies and a real data application demonstrate the effectiveness of the suggested model diagnostics.

scholarly journals Big-But-Biased Data Analytics for Air Quality

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1551
Author(s):  
Laura Borrajo ◽  
Ricardo Cao
Keyword(s):  
Air Quality ◽  
Data Analytics ◽  
Mean Squared Error ◽  
Smart Cities ◽  
Real Data ◽  
Cumulative Distribution ◽  
Simple Random Sample ◽  
Urban Air ◽  
Data Set ◽  
The Mean

Air pollution is one of the big concerns for smart cities. The problem of applying big data analytics to sampling bias in the context of urban air quality is studied in this paper. A nonparametric estimator that incorporates kernel density estimation is used. When ignoring the biasing weight function, a small-sized simple random sample of the real population is assumed to be additionally observed. The general parameter considered is the mean of a transformation of the random variable of interest. A new bootstrap algorithm is used to approximate the mean squared error of the new estimator. Its minimization leads to an automatic bandwidth selector. The method is applied to a real data set concerning the levels of different pollutants in the urban air of the city of A Coruña (Galicia, NW Spain). Estimations for the mean and the cumulative distribution function of the level of ozone and nitrogen dioxide when the temperature is greater than or equal to 30 ∘C based on 15 years of biased data are obtained.

scholarly journals Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Mursala Khan ◽  
Rajesh Singh
Keyword(s):  
Finite Population ◽  
Real Data ◽  
Survey Sampling ◽  
Systematic Sampling ◽  
Auxiliary Variables ◽  
Data Set ◽  
Population Mean ◽  
First Order ◽  
The Mean ◽  
A Chain

A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

scholarly journals Modified Ridge Regression Estimator with the Application of Peanut Production in Pakistan

2019 ◽  
pp. 1-8
Author(s):  
Asifa Mubeen ◽  
Nasir Jamal ◽  
Muhammad Hanif ◽  
Usman Shahzad
Keyword(s):  
Ridge Regression ◽  
Real Data ◽  
Production Data ◽  
Regression Estimator ◽  
Mean Square ◽  
Data Set ◽  
Regression Estimators ◽  
Peanut Production ◽  
Ridge Regression Estimator ◽  
The Mean

The main objective of the present study was to develop a new ridge regression estimator and fit the ridge regression model to the peanut production data of Pakistan. Peanut production data has been used to analyze the results. The data has been taken peanut production and growth rate of Pakistan. The mean square error of the proposed estimator is compared with some existing ridge regression estimators. In this study, we proposed a ridge regression estimator. The properties of proposed estimators are also discussed. The real data set of peanut production is used for assuming the performance of proposed and existing estimators. Numerical results of real data set show that proposed ridge regression estimator provides best results as compare to reviewed ones.

scholarly journals Regression Estimator Using Double Ranked Set Sampling

2002 ◽  
Vol 7 (2) ◽  
pp. 311
Author(s):  
Hani M. Samawi ◽  
Eman M. Tawalbeh
Keyword(s):  
Correlation Coefficient ◽  
Real Data ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Regression Estimator ◽  
Primary Analysis ◽  
Data Set ◽  
Population Mean ◽  
The Mean

The performance of a regression estimator based on the double ranked set sample (DRSS) scheme, introduced by Al-Saleh and Al-Kadiri (2000), is investigated when the mean of the auxiliary variable X is unknown. Our primary analysis and simulation indicates that using the DRSS regression estimator for estimating the population mean substantially increases relative efficiency compared to using regression estimator based on simple random sampling (SRS) or ranked set sampling (RSS) (Yu and Lam, 1997) regression estimator.  Moreover, the regression estimator using DRSS is also more efficient than the naïve estimators of the population mean using SRS, RSS (when the correlation coefficient is at least 0.4) and DRSS for high correlation coefficient (at least 0.91.) The theory is illustrated using a real data set of trees.  

scholarly journals Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study

2014 ◽  
Vol 44 (1) ◽  
pp. 33-46
Author(s):  
Jehad Al-Jararha ◽  
Ala' Bataineh
Keyword(s):  
Finite Population ◽  
Real Data ◽  
Auxiliary Variable ◽  
Data Set ◽  
Population Total ◽  
The Mean ◽  
Bias Variance ◽  
Highly Correlated ◽  
Population Ratio ◽  
Definition Of

The estimation of the population total $t_y,$ by using one or moreauxiliary variables, and the population ratio $\theta_{xy}=t_y/t_x,$$t_x$ is the population total for the auxiliary variable $X$, for afinite population are heavily discussed in the literature. In thispaper, the idea of estimation the finite population ratio$\theta_{xy}$ is extended to use the availability of auxiliaryvariable $Z$ in the study, such auxiliary variable  is not used inthe definition of the population ratio. This idea may be  supported by the fact that the variable $Z$  is highly correlated with the interest variable $Y$ than the correlation between the variables $X$ and $Y.$ The availability of such auxiliary variable can be used to improve the precision of the estimation of the population ratio.  To our knowledge, this idea is not discussed in the literature.  The bias, variance and the mean squares error  are given for our approach. Simulation from real data set,  the empirical relative bias and  the empirical relative mean squares error are computed for our approach and different estimators proposed in the literature  for estimating the population ratio $\theta_{xy}.$ Analytically and the simulation results show that, by suitable choices, our approach gives negligible bias and has less mean squares error.  

Acceptance sampling plans based on truncated life tests for Rama distribution

2019 ◽  
Vol 36 (7) ◽  
pp. 1181-1191 ◽  
Author(s):  
Amer Al-Omari ◽  
Amjad Al-Nasser ◽  
Enrico Ciavolino
Keyword(s):  
Life Time ◽  
Real Data ◽  
Acceptance Sampling ◽  
Data Set ◽  
Sampling Plans ◽  
Content Type ◽  
Acceptance Sampling Plans ◽  
Industry Applications ◽  
The Mean ◽  
Engineering Insurance

Purpose Lifetime data are used in many different applied sciences, like biomedicine, engineering, insurance and finance and others. The purpose of this paper is to develop a new acceptance sampling plans for Rama distribution when the mean lifetime test is truncated at a pre-determined time. The minimum sample sizes required to assert the specified life mean is obtained for a given customer’s risk. The operating characteristic function values of the sampling plans and producer’s risk are calculated. Design/methodology/approach The results are illustrated using numerical examples and a real data set is considered to illustrate the performance of the suggested acceptance sampling plans and how it can be used for the industry applications. Findings This paper shows a new acceptance sampling plans based on Rama distribution in the particular case when the mean life time test is truncated. Originality/value The results calculated in this paper demonstrate the differences between OC values for different distributions taken into account. In particular, OC values of Rama distribution are found to be less than the proposed distribution counterparts.

scholarly journals AN APPLICATION OF THE POISSON-WEIBULL MODEL FOR CENSURED DATA

2021 ◽  
Vol 39 (4) ◽  
pp. 505-521
Author(s):  
Valdemiro Piedade VIGAS ◽  
Fábio PRATAVIERA ◽  
Giovana Oliveira SILVA
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Survival Data ◽  
Real Data ◽  
Weibull Model ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Kaplan Meier ◽  
Proposed Model ◽  
The Mean

In this paper, we proposed the Poisson-Weibull distribution for the modeling of survival data. The motivation to study this model since, in addition to generalizing the Weibull distribution, which is widely used in several areas of knowledge among them the Survival and Reliability analysis, it presents great exibility in the forms of the hazard function. The Poisson-Weibull distribution was created in a composition of discrete and continuous distributions where there is no information about which factor was responsible for the component failure, only the minimum lifetime value among all risks is observed. The maximum likelihood approach was used to estimate the parameters of the model. Also was conducted a simulation study to examine the mean, the bias, and the root of the mean square error of the maximum likelihood estimates of the proposed model according to the censoring percentages and sample sizes. The model selection criteria were also applied, in addition to graphic techniques such as TTT-Plot and Kaplan-Meier. Application to the real data set was used to illustrate the usefulnessof the distribution.

scholarly journals Two-Parameter Stochastic Weibull Diffusion Model: Statistical Inference and Application to Real Modeling Example

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 160 ◽  
Author(s):  
Ahmed Nafidi ◽  
Meriem Bahij ◽  
Ramón Gutiérrez-Sánchez ◽  
Boujemâa Achchab
Keyword(s):  
Density Function ◽  
Real Data ◽  
Mean Value ◽  
Data Set ◽  
Trend Function ◽  
Error Measures ◽  
The Mean ◽  
Modeling Data ◽  
Two Parameter ◽  
Annealing Method

This paper describes the use of the non-homogeneous stochastic Weibull diffusion process, based on the two-parameter Weibull density function (the trend of which is proportional to the two-parameter Weibull probability density function). The trend function (conditioned and non-conditioned) is analyzed to obtain fits and forecasts for a real data set, taking into account the mean value of the process, the maximum likelihood estimators of the parameters of the model and the computational problems that may arise. To carry out the task, we employ the simulated annealing method for finding the estimators values and achieve the study. Finally, to evaluate the capacity of the model, the study is applied to real modeling data where we discuss the accuracy according to error measures.

scholarly journals A New Generating Family of Distributions: Properties and Applications to the Weibull Exponential Model

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
El-Sayed A. El-Sherpieny ◽  
Salwa Assar ◽  
Tamer Helal
Keyword(s):  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Exponential Model ◽  
Rate Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Set ◽  
Rate Functions ◽  
Family Of Distributions

A new method for generating family of distributions was proposed. Some fundamental properties of the new proposed family include the quantile, survival function, hazard rate function, reversed hazard and cumulative hazard rate functions are provided. This family contains several new models as sub models, such as the Weibull exponential model which was defined and discussed its properties. The maximum likelihood method of estimation is using to estimate the model parameters of the new proposed family. The flexibility and the importance of the Weibull-exponential model is assessed by applying it to a real data set and comparing it with other known models.

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