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## Robust confidence intervals for the difference of two independent population variances

#### Hayriye Esra AKYÜZ [1] , Prof. Dr. Hamza GAMGAM [2]

In this study, we propose confidence intervals and their bootstrap versions for the difference of variances of two independent population using some robust variance estimators. The proposed confidence intervals are compared with Herbert confidence interval in terms of coverage probability and average width. A simulation study is conducted to evaluate performances of the proposed confidence intervals under different scenarios. The simulation results indicate that the coverage probabilities for the proposed confidence intervals are very close to nominal confidence levels when the difference of population variances is zero. Confidence interval based on binary distance produces the narrowest average widths. Herbert confidence interval have not perform well for skewed distribution populations. Confidence interval based on comedian is generally recommended when the difference of population variances for skewed distributions is not zero. Average widths of bootstrap percentile confidence intervals are smaller, and decreases as sample size and nominal size increases, as expected. Consequently, we recommend bootstrap percentile confidence interval based on binary distances for skewed distributions.
Average width, Bootstrap percentile, Coverage probability, Robust estimator, Confidence interval
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Primary Language en Statistics and Probability Statistics Orcid: 0000-0002-1784-5910Author: Hayriye Esra AKYÜZ (Primary Author)Institution: BITLIS EREN UNIVERSITYCountry: Turkey Orcid: 0000-0002-9595-9315Author: Prof. Dr. Hamza GAMGAM Institution: Gazı UniversityCountry: Turkey Publication Date : February 6, 2020
 Bibtex @research article { hujms475318, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {478 - 493}, doi = {10.15672/hujms.475318}, title = {Robust confidence intervals for the difference of two independent population variances}, key = {cite}, author = {AKYÜZ, Hayriye Esra and GAMGAM, Prof. Dr. Hamza} } APA AKYÜZ, H , GAMGAM, P . (2020). Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 478-493 . DOI: 10.15672/hujms.475318 MLA AKYÜZ, H , GAMGAM, P . "Robust confidence intervals for the difference of two independent population variances". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 478-493 Chicago AKYÜZ, H , GAMGAM, P . "Robust confidence intervals for the difference of two independent population variances". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 478-493 RIS TY - JOUR T1 - Robust confidence intervals for the difference of two independent population variances AU - Hayriye Esra AKYÜZ , Prof. Dr. Hamza GAMGAM Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.475318 DO - 10.15672/hujms.475318 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 478 EP - 493 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.475318 UR - https://doi.org/10.15672/hujms.475318 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Robust confidence intervals for the difference of two independent population variances %A Hayriye Esra AKYÜZ , Prof. Dr. Hamza GAMGAM %T Robust confidence intervals for the difference of two independent population variances %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.475318 %U 10.15672/hujms.475318 ISNAD AKYÜZ, Hayriye Esra , GAMGAM, Prof. Dr. Hamza . "Robust confidence intervals for the difference of two independent population variances". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 478-493 . https://doi.org/10.15672/hujms.475318 AMA AKYÜZ H , GAMGAM P . Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 478-493. Vancouver AKYÜZ H , GAMGAM P . Robust confidence intervals for the difference of two independent population variances. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 493-478.

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