<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR"^^ . "Lognormal distribution is one of continuous distributions which has two\r\nparameters, namely μ dan σ\r\n2\r\n. In this research, we conducted an estimation of\r\n\r\nparameter σ\r\n\r\n2 of lognormal distribution using Bayesian method which is done by\r\ncombining the sample distribution and prior distribution to obtain the posterior\r\ndistribution. Here we used two kinds of priors, namely non-informative prior used\r\nis the Jeffrey's method and conjugate priors used is the inverse-gamma distribution.\r\nThe purpose of this research is to find the Bayesian estimate of parameter σ\r\n2 of\r\nlognormal distribution using the two priors, also to see how the characteristics of\r\nboth estimators analytically and empirically (by simulation study). Finally, the\r\nresults are compared to know which prior is better for estimating the parameter σ\r\n2\r\n\r\nof lognormal distribution.\r\nThe estimator of parameter σ\r\n\r\n2 using the non-informative prior is σ̂2\r\nNI =\r\n\r\n1\r\nn−1\r\n[∑ (ln 2xi\r\n)\r\nn\r\ni=1 −\r\n(∑ ln xi\r\nn\r\ni=1\r\n)\r\n2\r\nn\r\n]. While using the conjugate prior we obtained\r\n\r\nσ̂2\r\nK =\r\n2β\r\n(2α+n)\r\n+\r\n1\r\n(2α+n)\r\n[∑ (ln x − μ)\r\nn 2\r\ni=1\r\n\r\n]. The former is an unbiased estimator and\r\nthe later is an asymptotically unbiased estimator, and both estimators are consistent\r\nestimators. Then, based on the value of MSE (by simulation study), both estimators\r\nare good estimator of σ\r\n\r\n2 of lognormal distribution.\r\n\r\nKey Words: Lognormal Distribution, Bayesian Method, Non-Informative Prior,\r\nConjugate Prior, Inverse-Gamma Distribution, Characteristics of Estimator.\r\n\r\n\r\nDistribusi lognormal merupakan salah satu distribusi kontinu yang memiliki dua\r\nparameter, yaitu μ dan σ\r\n2\r\n. Pada penilitian ini, akan diduga parameter σ\r\n2 dari\r\ndistribusi lognormal menggunakan metode Bayes yang dilakukan dengan\r\nmenggabungkan distribusi sampel dan distribusi prior, sehingga diperoleh\r\ndistribusi posterior. Distribusi prior yang digunakan adalah prior non-informatif\r\nyang diperoleh dengan menggunakan metode Jeffrey’s dan prior konjugat dengan\r\ndistribusi invers-gamma.\r\nTujuan penelitian ini adalah untuk mengetahui nilai dugaan dari parameter σ\r\n2\r\ndistribusi lognormal menggunakan kedua prior tersebut. Kemudian, akan dilihat\r\njuga bagaimana sifat-sifat karakteristik penduga dari kedua prior tersebut baik\r\nsecara analitik maupun empirik dalam studi simulasi. Setelah itu, akan\r\ndibandingkan prior mana yang lebih baik digunakan untuk menduga parameter σ\r\n2\r\n\r\ndari distribusi lognormal berdasarkan nilai MSE-nya.\r\nEstimasi titik dari parameter σ\r\n\r\n2 untuk prior non-informatif, yaitu σ̂2\r\nNI =\r\n\r\n1\r\nn−1\r\n[∑ (ln 2xi\r\n)\r\nn\r\ni=1 −\r\n(∑ ln xi\r\nn\r\ni=1\r\n)\r\n2\r\nn\r\n]. Sedangkan untuk prior konjugat diperoleh\r\n\r\nestimasi titik dari parameter σ\r\n2\r\nadalah σ̂2\r\nK =\r\n2β\r\n(2α+n)\r\n+\r\n1\r\n(2α+n)\r\n[∑ (ln x − μ)\r\nn 2\r\ni=1\r\n\r\n].\r\n\r\nPenduga σ̂2\r\nNI dan σ̂2\r\nK secara berturut-turut merupakan penduga yang bersifat tak\r\nbias dan tak bias secara asimtotik serta kedua penduga merupakan penduga yang\r\nkonsisten. Kemudian berdasarkan nilai MSE pada studi simulasi, kedua prior baik\r\ndigunakan untuk menduga parameter σ\r\n\r\n2 dari distribusi lognormal.\r\n\r\nKata Kunci: Distribusi Lognormal, Metode Bayes, Prior Non-Informatif, Prior\r\nKonjugat, Distribusi Invers-Gamma, Karakteristik Penduga."^^ . "2020-04-03" . . . . . "FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM"^^ . . . . . . . "1617031105"^^ . "Hilda Venelia"^^ . "1617031105 Hilda Venelia"^^ . . . . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (File PDF)"^^ . . . "1. ABSTRAK - Hilda Venelia.pdf"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (File PDF)"^^ . . . "3. SKRIPSI FULL TANPA BAB PEMBAHASAN - Hilda Venelia.pdf"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (File PDF)"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "preview.jpg"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "medium.jpg"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "small.jpg"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "preview.jpg"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "medium.jpg"^^ . . . "PARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION\r\nUSING BAYESIAN METHOD WITH NON-INFORMATIVE\r\n\r\nPRIOR AND CONJUGATE PRIOR (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #58528 \n\nPARAMETER ESTIMATION OF LOGNORMAL DISTRIBUTION \nUSING BAYESIAN METHOD WITH NON-INFORMATIVE \n \nPRIOR AND CONJUGATE PRIOR\n\n" . "text/html" . . . "500 ilmu pengetahuan alam dan matematika" . . . "510 Matematika" . .