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## Determination of the Confidence Intervals for Multimodal Probability Density Functions

#### ORHAN KESEMEN [1] , BUĞRA KAAN TİRYAKİ [2] , EDA ÖZKUL [3] , ÖZGE TEZEL [4]

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The shortest interval approach can be solved as an optimization problem, while the equally tailed approach is determined by using the distribution function. The equal density approach is proposed instead of the optimization problem for determining the shortest confidence interval. It is applied to multimodal probability density functions to determine the shortest confidence interval. Furthermore, the equal density and optimization approach for the shortest confidence interval and the equally tailed approach were applied to numerical examples and their results were compared. Nevertheless, the main subject of this study is the calculation of the shortest confidence intervals for any multimodal distribution.

Multimodal probability density function, Confidence interval estimators, The shortest confidence interval, The equally tailed confidence interval, The equal density confidence interval
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Konular Statistics Yazar: ORHAN KESEMENKurum: KARADENIZ TECHNICAL UNIVERSITYÜlke: Turkey Yazar: BUĞRA KAAN TİRYAKİKurum: KARADENIZ TECHNICAL UNIVERSITYÜlke: Turkey Yazar: EDA ÖZKULKurum: KARADENIZ TECHNICAL UNIVERSITYÜlke: Turkey Yazar: ÖZGE TEZELKurum: KARADENIZ TECHNICAL UNIVERSITYÜlke: Turkey
 Bibtex @araştırma makalesi { gujs354422, journal = {Gazi University Journal of Science}, issn = {}, eissn = {2147-1762}, address = {Gazi Üniversitesi}, year = {}, volume = {31}, pages = {310 - 326}, doi = {}, title = {Determination of the Confidence Intervals for Multimodal Probability Density Functions}, key = {cite}, author = {TEZEL, ÖZGE and KESEMEN, ORHAN and ÖZKUL, EDA and TİRYAKİ, BUĞRA} } APA KESEMEN, O , TİRYAKİ, B , ÖZKUL, E , TEZEL, Ö . (). Determination of the Confidence Intervals for Multimodal Probability Density Functions. Gazi University Journal of Science, 31 (1), 310-326. Retrieved from http://dergipark.gov.tr/gujs/issue/35772/354422 MLA KESEMEN, O , TİRYAKİ, B , ÖZKUL, E , TEZEL, Ö . "Determination of the Confidence Intervals for Multimodal Probability Density Functions". Gazi University Journal of Science 31 (): 310-326 Chicago KESEMEN, O , TİRYAKİ, B , ÖZKUL, E , TEZEL, Ö . "Determination of the Confidence Intervals for Multimodal Probability Density Functions". Gazi University Journal of Science 31 (): 310-326 RIS TY - JOUR T1 - Determination of the Confidence Intervals for Multimodal Probability Density Functions AU - ORHAN KESEMEN , BUĞRA KAAN TİRYAKİ , EDA ÖZKUL , ÖZGE TEZEL Y1 - 2019 PY - 2019 N1 - DO - T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 310 EP - 326 VL - 31 IS - 1 SN - -2147-1762 M3 - UR - Y2 - 2017 ER - EndNote %0 Gazi University Journal of Science Determination of the Confidence Intervals for Multimodal Probability Density Functions %A ORHAN KESEMEN , BUĞRA KAAN TİRYAKİ , EDA ÖZKUL , ÖZGE TEZEL %T Determination of the Confidence Intervals for Multimodal Probability Density Functions %D 2019 %J Gazi University Journal of Science %P -2147-1762 %V 31 %N 1 %R %U ISNAD KESEMEN, ORHAN , TİRYAKİ, BUĞRA , ÖZKUL, EDA , TEZEL, ÖZGE . "Determination of the Confidence Intervals for Multimodal Probability Density Functions". Gazi University Journal of Science 31 / 1 310-326.