Background: Most investigators use ordinary least squares (OLS) methods to model low birth weight. When the data are non-normal or contain outliers, OLS become ineffective. However, the quantile method of forecasting low birth weight has not been fully evaluated, although it has good potential for overcoming problems associated with linear regression. Methods: The present study reports our comparison between the OLS and quantile regression methods for modeling low birth weight when the data are right skewed and outliers are presented. Additionally, we evaluated the performance of the associated algorithm in recovering the true parameter using the bootstrap method. Results: Our study found that a mother's education level, the number of maternal parities, and the last birth interval significantly impacted low birth weight at any selected low quantile. Based on the bootstrap simulation study, the proposed model was considered to be acceptable since both methods generated nearly identical estimates of the parameter model. An accuracy test proved that the quantile method was an unbiased estimator. Conclusions: The present study found that low birth weight is significantly affected by the mother's educational level, the number of maternal parities, and the last birth interval.

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This present study purposes to conduct Bayesian inference to estimate scale parameters, denoted by θ, with known location parameter or β, of Weibull distribution. There are two types of prior distributions used in this study, conjugate prior and non informative prior. As conjugate prior is inverse gamma, and as non-informative prior is Jeffreys' prior. This research also aims to study several theoretical properties of posterior distribution based on prior used implement it to generated data and make comparison between both Bayes estimator as well. The method used to evaluate as the best estimator is based on the smallest Mean Square Error (MSE) value. This study proveds that Bayes estimator using conjugate prior produces better estimated parameter value estimate non-informative prior since it produces smaller MSE value, for condition θ > 1 based on analytic and simulation study. Meanwhile for θ < 1 both priors could not yield acceptable estimated parameter value.

Abstrak. Portofolio merupakan kumpulan dari beberapa investasi saham. Portofolioterbaik adalah portofolio dengan mean return dan risiko saham yang terbaik. Salah satumetode dalam mengukur nilai risiko adalah dengan Value at Risk (VaR). VaR didenisikansebagai tingkat kerugian maksimal atau return minimal pada tingkat kepercayaanyang cukup tinggi untuk waktu tertentu. Jika seorang investor membentuk portofoliomaka berarti investor menentukan proporsi dana yang diinvestasikan pada masingmasingsaham. Investor menginvestasikan dana pada masing-masing saham dengan totalproporsi dana adalah 1. Permasalahan dalam menghitung proporsi dana dapat menggunakanmetode Pengganda Lagrange. Dari 33 saham Perbankan yang terdaftar padaBursa Efek Indonesia didapat komposisi portofolio yang terdiri dari Bank DanamonIndonesia Tbk, Bank Mandiri (Persero) Tbk dan Bank CIMB Niaga Tbk. Dari ketigasaham diperoleh proporsi investasi masing-masing dana yaitu 19,76% Bank DanamonIndonesia Tbk, 60,34% Bank Mandiri (Persero) Tbk dan 19,90% Bank CIMB Niaga Tbk.Dari portofolio yang terbentuk didapat nilai risiko yaitu 0,001345. Hal ini berarti risikodari portofolio yang terbentuk sangat kecil yaitu 0,13% sehingga aman bagi investordalam berinvestasi.Kata Kunci: Portofolio, Value at Risk, Pengganda Lagrange, Risiko

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