# KAJIAN SIMULASI PENDUGAAN SELANG KEPERCAYAAN BOOTSTRAP BAGI ARAH MEDIAN DATA SIRKULAR

• Cici Suhaeni Institut Pertanian Bogor (IPB)
• I Made Sumertajaya Institut Pertanian Bogor (IPB)
• Anik Djuraidah
Keywords: bootstrap confidence interval, circular data, circular statistics, median direction

### Abstract

The median direction is one of central tendency of circular data. The estimation process usually requires information about sampling distribution of statistic that want to be used as a parameter estimate. Theoretically, sampling distribution derived from population distribution. But, it is not easy to get sampling distribution of median although the population distribution is known.  When the sampling distribution cannot be derived easily from population distribution, the bootstrap method can be an alternative to handle it. This study wants to evaluate the effect of increasing concentration parameter to the performance of bootstrap confidence interval estimation for median direction through simulation study. Three methods were used to estimate the interval  which are equal-tailed arc (ETA), symmetric arc (SYMA), and likelihood-based arc (LBA). The most important criterion to evaluate them were true coverage and interval width. The simulation results that in general, the increasing of concentration parameter followed by  more narrow interval. For small concentration parameter (k<1), all methods give unstable true coverage and interval width. The authors also identify that those three methods produce intervals with identical width when the parameter concentration is 20 or more. In terms of coverage and interval width, the best method was ETA.

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Published
2018-04-30
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