Confidence Interval for the Mean of a Contaminated Normal Distribution

Abu-Shawie, M. O.; Al-Athari, Faris M.; Kittani, Hilmi F.

doi:10.3923/jas.2009.2835.2840

Cited by 20 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 below shows the median accuracy (left) and the median NMI (right) for the time series with five discrete levels and various ratios of outliers. The error bars indicate the 95% median absolute deviation (MAD) t confidence interval [14].…”

Section: E Experiments With the Enduring-state Datasetmentioning

confidence: 99%

A Bayesian Hybrid Approach to Unsupervised Time Series Discretization

Kameya

Synnaeve

Doncescu³

et al. 2010

2010 International Conference on Technologies and Applications of Artificial Intelligence

View full text Add to dashboard Cite

Abstract-Discretization is a key preprocessing step in knowledge discovery to make raw time series data applicable to symbolic data mining algorithms. To improve the comprehensibility of the mined results, or to help the induction step of the mining algorithms, in discretization, it is natural to prefer having discrete levels which can be mapped into intuitive symbols. In this paper, we aim to make smoothing of the data points along with the time axis, and make binning or clustering at the measurement axis. In particular, we propose a hybrid discretization method based on variational Bayes, in which the output of one discretization method is smoothly exploited as hyperparameters of another probabilistic discretization model such as a continuous hidden Markov model. The experiments with artificial and real datasets exhibit the usefulness of this hybrid approach.

show abstract

Section: E Experiments With the Enduring-state Datasetmentioning

confidence: 99%

A Bayesian Hybrid Approach to Unsupervised Time Series Discretization

Kameya

Synnaeve

Doncescu³

et al. 2010

2010 International Conference on Technologies and Applications of Artificial Intelligence

View full text Add to dashboard Cite

show abstract

“…Johnson (1978) proposed a modification of the Student's t confidence interval for skewed distributions. Since Johnson (1978), many researchers have obtained confidence intervals for population mean of a skewed distribution (Chen, 1995;Meeden, 1999;Kibria, 2006;Shi and Kibria, 2007;Baklizi, 2008;Abu-Shawiesh et al, 2009;Baklizi and Kibria, 2009;Abu-Shawiesh et al, 2011;Pek et al, 2017;Abu-Shawiesh et al, 2018;Abu-Shawiesh and Saghir, 2019;Akyuz and Abu-Shawiesh, 2020;Sinsomboonthong et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

A modified robust confidence interval for the population mean of distribution based on deciles

Abu-Shawiesh

Sinsomboonthong

Kibria

2022

Statistics in Transition New Series

View full text Add to dashboard Cite

The confidence interval is an important statistical estimator of population location and dispersion parameters. The paper considers a robust modified confidence interval, which is an adjustment of the Student’s t confidence interval based on the decile mean and decile standard deviation for estimating the population mean of a skewed distribution. The efficiency of the proposed interval estimator is evaluated on the basis of an extensive Monte Carlo simulation study. The coverage ratio and average width of the proposed confidence interval are compared with certain existing and widely used confidence intervals. The simulation results show that, in general, the proposed interval estimator’s performance is highly effective. For illustrative purposes, three real-life data sets are analyzed, which, to a certain extent, support the findings obtained from the simulation study. Thus, we recommend that practitioners use the robust modified confidence interval for estimating the population mean when the data are generated by a normal or skewed distribution.

show abstract

“…is the sample standard deviation and t(α/2,n−1) is the upper percentage point of the Student-t distribution with (n -1) degrees of freedom, i.e. P(t > t(α,n−1)) = α (Abu-Shawiesh et al, 2009;Bonett & Seier, 2003). The Student-t distribution was developed by William Gosset in 1908 as a more robust way of testing hypotheses specifically when sample sizes are below 30 (Student, 1908).…”

Section: Introductionmentioning

confidence: 99%

Robust Confidence Intervals for the Population Mean Alternatives to the Student-t Confidence Interval

Abu-Shawiesh

Saghir

2020

J. Mod. Appl. Stat. Methods

View full text Add to dashboard Cite

In this paper, three robust confidence intervals are proposed as alternatives to the Student t confidence interval. The performance of these intervals was compared through a simulation study shows that Qn-t confidence interval performs the best and it is as good as Student’s t confidence interval. Real-life data was used for illustration and performing a comparison that support the findings obtained from the simulation study.

show abstract

Confidence Interval for the Mean of a Contaminated Normal Distribution

Cited by 20 publications

References 19 publications

A Bayesian Hybrid Approach to Unsupervised Time Series Discretization

A Bayesian Hybrid Approach to Unsupervised Time Series Discretization

A modified robust confidence interval for the population mean of distribution based on deciles

Robust Confidence Intervals for the Population Mean Alternatives to the Student-t Confidence Interval

Contact Info

Product

Resources

About