A New Statistical Model for Predicting Customer Octane Satisfaction Using Trained-Rater Observations

Rodriguez, Robert N.; Taniguchi, Brian Y.

doi:10.4271/801356

Cited by 6 publications

(5 citation statements)

References 6 publications

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“…. , x n ) be a random sample from a Burr XII distribution with the density function given in Equation (2) and assume that the shape parameters c and k are unknown. The ML estimators for c and k can be obtained by maximizing the following log-likelihood function:…”

Section: Parameters Estimationmentioning

confidence: 99%

“…This corresponds to multiplying the largest observation by some large values. To evaluate the performance of these estimators, the bias and root mean square errors (RMSE) were calculated using 1000 replications for the sample sizes n = 25, 50, 100 and the parameter values (2,5) and (5,2). The bias and RMSE are calculated using…”

Section: Simulationmentioning

confidence: 99%

“…Here, c and k are the shape parameters and θ = (c, k) T . Figure 1 depicts some examples of the Burr XII density function given in Equation (2). From these plots we can observe how the shape parameters c and k affect the peakedness, skewness and the tail thickness of the Burr XII distribution.…”

Section: Introductionmentioning

confidence: 97%

“…[1] This distribution, which is a special case of the Generalized Beta type II (GB2) distribution, is also known as 'Singh-Maddala' distribution. It has been widely used as a model in areas such as business, [2] economics, [3] engineering, [4] finance, [4] hydrology, [5] mineralogy, [6] medical research, [7] and reliability analysis. [7][8][9][10] Its properties have been studied by Burr and Cislak [11] and Al-Hussaini.…”

Section: Introductionmentioning

confidence: 99%

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Optimal B-robust estimators for the parameters of the Burr XII distribution

Doğru

Arslan

2015

Journal of Statistical Computation and Simulation

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The Burr XII distribution offers a flexible alternative to the distributions that play important role for modelling data in reliability, risk and process capability. However, estimating the shape parameters of the Burr XII distribution is a challenging problem. The classical estimation methods such as maximum likelihood and least squares are often used to estimate the parameters of the Burr XII distribution, but these methods are very sensitive to the outliers in the data. Thus, a robust estimation method alternative to the classical methods is needed to find robust estimators that are less sensitive to the outliers in the data. The purpose of this paper is to use the optimal B-robust estimation method [Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA. Robust statistics: the approach based on influence functions. New York: Wiley; 1986] to obtain robust estimators for the shape parameters of the Burr XII distribution. The simulation results show that the optimal B-robust estimators generally outperform the classical estimators in terms of the bias and root mean square errors when there are outliers in data.

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Section: Parameters Estimationmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal B-robust estimators for the parameters of the Burr XII distribution

Doğru

Arslan

2015

Journal of Statistical Computation and Simulation

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“…However, in recent years, this distribution has been used in a variety of fields such as business Rodriguez and Taniguchi (1980). Economics and finance McDonald and Richards (1987).…”

Section: Introductionmentioning

confidence: 99%

On the Product and Ratio of Two Generalized Order Statistics From the Generalized Burr Type-Ii Distribution

Maswadah¹

2013

Journal of Mathematics and Statistics

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In this study, the probability density functions of the product and quotient of two generalized order statistics from the generalized Burr Type-XII distribution have been derived, using the Mellin transform and its inverse. Several interesting special cases have also been obtained such as the product and quotient of extreme generalized order statistics and the product and quotient of consecutive generalized order statistics

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Simple Forms of the Bivariate Density Function

Balakrishna

Lai

2009

Continuous Bivariate Distributions

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A New Statistical Model for Predicting Customer Octane Satisfaction Using Trained-Rater Observations

Cited by 6 publications

References 6 publications

Optimal B-robust estimators for the parameters of the Burr XII distribution

Optimal B-robust estimators for the parameters of the Burr XII distribution

On the Product and Ratio of Two Generalized Order Statistics From the Generalized Burr Type-Ii Distribution

Simple Forms of the Bivariate Density Function

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