Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples

This study presents a novel methodology to investigate the nonparametric estimation of a survival probability under random censoring time using the ranked observations from a Partially Rank-Ordered Set (PROS) sampling design and employs it in a hematological disorder study. The PROS sampling design has numerous applications in medicine, social sciences and ecology where the exact measurement of the sampling units is costly; however, sampling units can be ordered by using judgment ranking or available concomitant information. The general estimation methods are not directly applicable to the case where samples are from rank-based sampling designs, because the sampling units do not meet the identically distributed assumption. We derive asymptotic distribution of a Kaplan-Meier (KM) estimator under PROS sampling design. Finally, we compare the performance of the suggested estimators via several simulation studies and apply the proposed methods to a real data set. The results show that the proposed estimator under rank-based sampling designs outperforms its counterpart in a simple random sample (SRS).

Download Full-text

A Novel Chen Extension: Theory, Characterizations and Different Estimation Methods

European Journal of Statistics ◽

10.28924/ada/stat.2.1 ◽

2021 ◽

Vol 2 ◽

pp. 1

Author(s):

Haitham M. Yousof ◽

Mustafa C. Korkmaz ◽

G.G. Hamedani ◽

Mohamed Ibrahim

Keyword(s):

Numerical Analysis ◽

Maximum Likelihood ◽

Weighted Least Squares ◽

Real Data ◽

Estimation Methods ◽

Simulation Studies ◽

Data Set ◽

Anderson Darling ◽

Mean Variance ◽

Skewness And Kurtosis

In this work, we derive a novel extension of Chen distribution. Some statistical properties of the new model are derived. Numerical analysis for mean, variance, skewness and kurtosis is presented. Some characterizations of the proposed distribution are presented. Different classical estimation methods under uncensored schemes such as the maximum likelihood, Anderson-Darling, weighted least squares and right-tail Anderson–Darling methods are considered. Simulation studies are performed in order to compare and assess the above-mentioned estimation methods. For comparing the applicability of the four classical methods, two application to real data set are analyzed.

Download Full-text

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.39 ◽

2020 ◽

pp. 507-522

Author(s):

Parisa Torkaman

Keyword(s):

Least Squares ◽

Exponential Distribution ◽

Mean Squared Error ◽

Weighted Least Squares ◽

Real Data ◽

Minimum Variance ◽

Cumulative Distribution ◽

Estimation Methods ◽

Data Set ◽

Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

Download Full-text

New Lindley Half Cauchy Distribution: Theory and Applications

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.d4734.119420 ◽

2020 ◽

Vol 9 (4) ◽

pp. 1-7

Keyword(s):

Maximum Likelihood ◽

Real Data ◽

Cauchy Distribution ◽

Least Square ◽

Cumulative Distribution ◽

Likelihood Method ◽

Estimation Methods ◽

Model Parameters ◽

Data Set ◽

Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

Download Full-text

Robustness of Projective IRT to Misspecification of the Underlying Multidimensional Model

Applied Psychological Measurement ◽

10.1177/0146621620909894 ◽

2020 ◽

Vol 44 (5) ◽

pp. 362-375

Author(s):

Tyler Strachan ◽

Edward Ip ◽

Yanyan Fu ◽

Terry Ackerman ◽

Shyh-Huei Chen ◽

...

Keyword(s):

Item Response Theory ◽

Item Response ◽

Real Data ◽

Model Parameters ◽

Simulation Studies ◽

Response Theory ◽

Computational Stability ◽

Data Set ◽

Response Data ◽

Higher Dimensional

As a method to derive a “purified” measure along a dimension of interest from response data that are potentially multidimensional in nature, the projective item response theory (PIRT) approach requires first fitting a multidimensional item response theory (MIRT) model to the data before projecting onto a dimension of interest. This study aims to explore how accurate the PIRT results are when the estimated MIRT model is misspecified. Specifically, we focus on using a (potentially misspecified) two-dimensional (2D)-MIRT for projection because of its advantages, including interpretability, identifiability, and computational stability, over higher dimensional models. Two large simulation studies (I and II) were conducted. Both studies examined whether the fitting of a 2D-MIRT is sufficient to recover the PIRT parameters when multiple nuisance dimensions exist in the test items, which were generated, respectively, under compensatory MIRT and bifactor models. Various factors were manipulated, including sample size, test length, latent factor correlation, and number of nuisance dimensions. The results from simulation studies I and II showed that the PIRT was overall robust to a misspecified 2D-MIRT. Smaller third and fourth simulation studies were done to evaluate recovery of the PIRT model parameters when the correctly specified higher dimensional MIRT or bifactor model was fitted with the response data. In addition, a real data set was used to illustrate the robustness of PIRT.

Download Full-text

Big-But-Biased Data Analytics for Air Quality

Electronics ◽

10.3390/electronics9091551 ◽

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.

Download Full-text

Mixture of Lindley and Inverse Weibull Distributions: Properties and Estimation

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2021.20.14 ◽

2021 ◽

Vol 20 ◽

pp. 134-143

Author(s):

A. S. Al-Moisheer ◽

A. F. Daghestani ◽

K. S. Sultan

Keyword(s):

Method Of Moments ◽

Generalized Method Of Moments ◽

Real Data ◽

Estimation Methods ◽

Simulation Studies ◽

Weibull Distributions ◽

Unknown Parameters ◽

Data Application ◽

Rate Functions ◽

And Behavior

In this paper, we talk about a mixture of one-parameter Lindley and inverse Weibull distributions (MLIWD). First, We introduce and discuss the MLIWD. Then, we study the main statistical properties of the proposed mixture and provide some graphs of both the density and the associated hazard rate functions. After that, we estimate the unknown parameters of the proposed mixture via two estimation methods, namely, the generalized method of moments and maximum likelihood. In addition, we compare the estimation methods via some simulation studies to determine the efficacy of the two estimation methods. Finally, we evaluate the performance and behavior of the proposed mixture with different numerical examples and real data application in survival analysis.

Download Full-text

HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

EPRA International Journal of Multidisciplinary Research (IJMR) ◽

10.36713/epra3291 ◽

2020 ◽

pp. 276-287

Author(s):

Arun Kumar Chaudhary ◽

Vijay Kumar

Keyword(s):

Exponential Distribution ◽

Likelihood Estimation ◽

Real Data ◽

Least Square ◽

Estimation Methods ◽

Logistic Distribution ◽

Model Parameters ◽

Type I ◽

Data Set ◽

Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

Download Full-text

Topp–Leone Linear Exponential Distribution

Stochastics and Quality Control ◽

10.1515/eqc-2017-0022 ◽

2018 ◽

Vol 33 (1) ◽

pp. 31-43

Author(s):

Bol A. M. Atem ◽

Suleman Nasiru ◽

Kwara Nantomah

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimation ◽

Exponential Distribution ◽

Likelihood Estimation ◽

Real Data ◽

Simulation Studies ◽

Finite Sample ◽

Data Set ◽

Finite Sample Properties ◽

Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

Download Full-text

A new class of skew-logistic distribution

Mathematical Sciences ◽

10.1007/s40096-019-00306-8 ◽

2019 ◽

Vol 13 (4) ◽

pp. 375-385

Author(s):

Saeed Mirzadeh ◽

Anis Iranmanesh

Keyword(s):

Exponential Family ◽

Real Data ◽

Statistical Characteristics ◽

Logistic Distribution ◽

Simulation Studies ◽

Data Set ◽

The Real ◽

New Class ◽

Skewness Parameter

Abstract In this study, the researchers introduce a new class of the logistic distribution which can be used to model the unimodal data with some skewness present. The new generalization is carried out using the basic idea of Nadarajah (Statistics 48(4):872–895, 2014), called truncated-exponential skew-logistic (TESL) distribution. The TESL distribution is a member of the exponential family; therefore, the skewness parameter can be derived easier. Meanwhile, some important statistical characteristics are presented; the real data set and simulation studies are applied to evaluate the results. Also, the TESL distribution is compared to at least five other skew-logistic distributions.

Download Full-text

Regularized Estimation of the Four-Parameter Logistic Model

Psych ◽

10.3390/psych2040020 ◽

2020 ◽

Vol 2 (4) ◽

pp. 269-278

Author(s):

Michela Battauz

Keyword(s):

Logistic Model ◽

Likelihood Function ◽

Latent Trait ◽

Real Data ◽

Theory Model ◽

Simulation Studies ◽

Data Set ◽

Penalty Term ◽

Regularized Estimation ◽

Item Parameters

The four-parameter logistic model is an Item Response Theory model for dichotomous items that limit the probability of giving a positive response to an item into a restricted range, so that even people at the extremes of a latent trait do not have a probability close to zero or one. Despite the literature acknowledging the usefulness of this model in certain contexts, the difficulty of estimating the item parameters has limited its use in practice. In this paper we propose a regularized estimation approach for the estimation of the item parameters based on the inclusion of a penalty term in the log-likelihood function. Simulation studies show the good performance of the proposal, which is further illustrated through an application to a real-data set.

Download Full-text