scholarly journals Monitoring Robust Estimates for Compositional Data

2021 ◽  
Vol 50 (2) ◽  
pp. 16-37
Author(s):  
Valentin Todorov
Keyword(s):  
Compositional Data ◽  
Real Life ◽  
R Package ◽  
Diagnostic Tools ◽  
Data Set ◽  
Mahalanobis Distances ◽  
Robust Estimates ◽  
Real Life Data ◽  
Manufactured Exports ◽  
Parameter Values

In a number of recent articles Riani, Cerioli, Atkinson and others advocate the technique of monitoring robust estimates computed over a range of key parameter values. Through this approach the diagnostic tools of choice can be tuned in such a way that highly robust estimators which are as efficient as possible are obtained. This approach is applicable to various robust multivariate estimates like S- and MM-estimates, MVE and MCD as well as to the Forward Search in whichmonitoring is part of the robust method. Key tool for detection of multivariate outliers and for monitoring of robust estimates is the Mahalanobis distances and statistics related to these distances. However, the results obtained with thistool in case of compositional data might be unrealistic since compositional data contain relative rather than absolute information and need to be transformed to the usual Euclidean geometry before the standard statistical tools can be applied. Various data transformations of compositional data have been introduced in the literature and theoretical results on the equivalence of the additive, the centered, and the isometric logratio transformation in the context of outlier identification exist. To illustrate the problem of monitoring compositional data and to demonstrate the usefulness of monitoring in this case we start with a simple example and then analyze a real life data set presenting the technologicalstructure of manufactured exports. The analysis is conducted with the R package fsdaR, which makes the analytical and graphical tools provided in the MATLAB FSDA library available for R users.

scholarly journals Calibration-Based Estimators using Different Distance Measures under Two Auxiliary Variables: A Comparative Study

2021 ◽  
Vol 19 (1) ◽  
pp. 2-20
Author(s):  
Piyush Kant Rai ◽  
Alka Singh ◽  
Muhammad Qasim
Keyword(s):  
Mean Squared Error ◽  
Real Life ◽  
Distance Functions ◽  
Distance Measures ◽  
Auxiliary Variables ◽  
Data Set ◽  
Life Data ◽  
Squared Error ◽  
Real Life Data ◽  
Relative Root

This article introduces calibration estimators under different distance measures based on two auxiliary variables in stratified sampling. The theory of the calibration estimator is presented. The calibrated weights based on different distance functions are also derived. A simulation study has been carried out to judge the performance of the proposed estimators based on the minimum relative root mean squared error criterion. A real-life data set is also used to confirm the supremacy of the proposed method.

PROFIT ESTIMATION FOR A PRODUCT UNDER WARRANTY: AN EVALUATION BASED ON CUSTOMER'S EXPECTATION AND SATISFACTION

2014 ◽  
Vol 21 (06) ◽  
pp. 1450029 ◽  
Author(s):  
P. K. KAPUR ◽  
ADARSH ANAND ◽  
NITIN SACHDEVA
Keyword(s):  
Real Life ◽  
Fixed Cost ◽  
Inventory Cost ◽  
Data Set ◽  
Customer Complaints ◽  
Customer Expectation ◽  
Real Life Data ◽  
Proposed Model ◽  
The Difference ◽  
Warranty Claims

Performance of a product not as expected by the customer brings warranty expenditure into the picture. In other words, the deviation of the product performance (PP) from the customer expectation (CE) is the reason for customer complaints and warranty expenses. When this conflicting scenario occurs in market, warranty comes into existence and fulfilling warranty claims of customers adds to product's overall cost. In this paper, based on the difference between PP and CE about the product we estimate profit for the firm. Furthermore, factors like fixed cost, production cost and inventory cost have also been considered in framing the optimization problem. In the proposed model, a two-dimensional innovation diffusion model (TD-IDM) which combines the adoption time of technological diffusion and price of the product has been used. Classical Cobb–Douglas function that takes into account the technological adoptions and other dimensions explicitly has been used to structure the production function. The proposed model has been validated on real life data set.

scholarly journals Bayesian Analysis of Extended Cox Model with Time-Varying Covariates Using Bootstrap Prior

2020 ◽  
Vol 18 (2) ◽  
pp. 2-13
Author(s):  
Oyebayo Ridwan Olaniran ◽  
Mohd Asrul Affendi Abdullah
Keyword(s):  
Empirical Bayes ◽  
Cox Model ◽  
Real Life ◽  
Estimation Procedure ◽  
Time Varying ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Time Varying Covariates ◽  
Extended Cox Model

A new Bayesian estimation procedure for extended cox model with time varying covariate was presented. The prior was determined using bootstrapping technique within the framework of parametric empirical Bayes. The efficiency of the proposed method was observed using Monte Carlo simulation of extended Cox model with time varying covariates under varying scenarios. Validity of the proposed method was also ascertained using real life data set of Stanford heart transplant. Comparison of the proposed method with its competitor established appreciable supremacy of the method.

scholarly journals A New Generalized Transmuted Inverse Exponential Distribution: Properties and Application

2018 ◽  
pp. 1-13
Author(s):  
Uchenna U. Uwadi ◽  
Elebe E. Nwaezza
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Real Life Data ◽  
Proposed Model ◽  
Inverse Exponential Distribution ◽  
The Moment

In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model.     

Rough ISODATA Algorithm

2013 ◽  
Vol 3 (4) ◽  
pp. 1-14 ◽  
Author(s):  
S. Sampath ◽  
B. Ramya
Keyword(s):  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Real Life ◽  
Vital Role ◽  
Data Sets ◽  
Clustering Method ◽  
Data Set ◽  
Number Of Clusters ◽  
Real Life Data ◽  
Nonparametric Statistical

Cluster analysis is a branch of data mining, which plays a vital role in bringing out hidden information in databases. Clustering algorithms help medical researchers in identifying the presence of natural subgroups in a data set. Different types of clustering algorithms are available in the literature. The most popular among them is k-means clustering. Even though k-means clustering is a popular clustering method widely used, its application requires the knowledge of the number of clusters present in the given data set. Several solutions are available in literature to overcome this limitation. The k-means clustering method creates a disjoint and exhaustive partition of the data set. However, in some situations one can come across objects that belong to more than one cluster. In this paper, a clustering algorithm capable of producing rough clusters automatically without requiring the user to give as input the number of clusters to be produced. The efficiency of the algorithm in detecting the number of clusters present in the data set has been studied with the help of some real life data sets. Further, a nonparametric statistical analysis on the results of the experimental study has been carried out in order to analyze the efficiency of the proposed algorithm in automatic detection of the number of clusters in the data set with the help of rough version of Davies-Bouldin index.

Conditional failure profile analysis for multiple failure modes from incomplete two-dimensionalwarranty data

2021 ◽  
pp. 1748006X2110397
Author(s):  
Sanjib Kumar Gupta
Keyword(s):  
Manufacturing Industry ◽  
Failure Modes ◽  
Profile Analysis ◽  
Real Life ◽  
Field Performance ◽  
Time Interval ◽  
Data Set ◽  
Testing Procedures ◽  
Real Life Data ◽  
Intangible Costs

This paper addresses the issue of detecting dominating failure modes of a system from a two-dimensional warranty data set by analyzing conditional failure profile of the system. Two testing procedures have been proposed to test whether any of the failure modes is dominating at a particular time interval and whether there is a change of the failure profile from one time interval to another disjoint time interval, conditioning on a given usage layer. Detecting the problematic failure modes early from the conditional failure profile and taking appropriate actions to reduce the conditional failure probability of the system can significantly reduce both tangible and intangible costs of poor reliability in any manufacturing industry. On the other hand, the study of possible changes of conditional failure profiles has a significant role to assess the field performance of items from one time interval to another time interval for a particular choice of usage layer. The utility of this study is explored with the help of a real-life data set.

scholarly journals Interval Estimations of the Two-Parameter Exponential Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Lai Jiang ◽  
Augustine C. M. Wong
Keyword(s):  
Exponential Distribution ◽  
Scale Parameter ◽  
Real Life ◽  
Simulation Studies ◽  
Threshold Parameter ◽  
Predictive Density ◽  
Data Set ◽  
Interval Estimates ◽  
Real Life Data ◽  
Two Parameter

In applied work, the two-parameter exponential distribution gives useful representations of many physical situations. Confidence interval for the scale parameter and predictive interval for a future independent observation have been studied by many, including Petropoulos (2011) and Lawless (1977), respectively. However, interval estimates for the threshold parameter have not been widely examined in statistical literature. The aim of this paper is to, first, obtain the exact significance function of the scale parameter by renormalizing thep∗-formula. Then the approximate Studentization method is applied to obtain the significance function of the threshold parameter. Finally, a predictive density function of the two-parameter exponential distribution is derived. A real-life data set is used to show the implementation of the method. Simulation studies are then carried out to illustrate the accuracy of the proposed methods.

scholarly journals Transmuted Alpha Power Inverse Rayleigh Distribution: Properties and Application

2019 ◽  
Vol 11 (2) ◽  
pp. 185-194
Author(s):  
A. S. Malik ◽  
S. P. Ahmad
Keyword(s):  
Parameter Estimation ◽  
Potential Application ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Parameter Distribution ◽  
Alpha Power ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Proposed Model

This paper proposes a new three parameter-distribution through the technique known as Transmutation. The proposed distribution is named Transmuted Alpha power inverse Rayleigh Distribution. Several important properties of the distribution are derived. The parameter estimation is also carried out. Two real life data set are used at the end to describe the potential application of proposed model.

scholarly journals Bayesian Multilevel Models for Count Data

2021 ◽  
pp. 224-233
Author(s):  
Olumide Sunday Adesina
Keyword(s):  
Count Data ◽  
Multilevel Models ◽  
Geometric Model ◽  
Real Life ◽  
Simulated Data ◽  
Data Set ◽  
K Value ◽  
Real Life Data ◽  
Level Model ◽  
Multi Level

The traditional Poisson regression model for fitting count data is considered inadequate to fit over-or under-dispersed count data and new models have been developed to make up for such inadequacies inherent in the model. In this study, Bayesian Multi-level model was proposed using the No-U-Turn Sampler (NUTS) sampler to sample from the posterior distribution. A simulation was carried out for both over-and under-dispersed data from discrete Weibull distribution. Pareto k diagnostics was implemented, and the result showed that under-dispersed and over-dispersed simulated data has all its k value to be less than 0.5, which indicate that all the observations are good. Also all WAIC were the same as LOO-IC except for Poisson in the over-dispersed simulated data. Real-life data set from National Health Insurance Scheme (NHIS) was used for further analysis. Seven multi-level models were f itted and the Geometric model outperformed other model. 

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