This final project discusses the increases of the sequence ⌊k √ n⌋ for any fixed positive integer k. For the increases of the sequence, the simplified expressions value of n (mod k) is given. This is a review of some parts of Hyatt and Skayers [Journal of Combinatorial Number Theory, 15 (2015), 1-12]. Furthermore, we provide the difference between the upper bound and lower bound of …
This nal project is a review of Kadilar and Chingi [Journal of Modern Applied Statistical Method, 35 (2006), 111{115] which discusses three estimators of ratio population variances ^ S2 KC1, ^ S2 K C2 and ^ S2 KC3 of the population of variables Y using known auxiliary variables X on simple random sampling. The three estimators ^ S2 K C1, ^ S2 KC2 and ^ S2 KC3 are the modied of ratio…
This final project discusses two estimators, which are [(¯yFT )D]k=1 and [(¯yFT )D]k=2. These two estimators have variables Y and imputated auxiliary variables X. Then bias and means square error (MSE) are shown. Furthermore MSE of these two estimators are compared. This comparison shows that the estimator which has the smallest MSE is relatively efficient. Keywords: Imputation, missing …
This nal project discusses a prime factor q of an odd perfect number x satisfying the inequality q < (3x)1=3. This is a review of some parts of Acquaah and Konyagin's paper [International Journal of Number Theory, 8 (2012), 1537- 1540]. The result of a prime factor of an odd perfect number x is determined by using the concept of the relationship between sigma function and perfect number. …
This final project discusses the estimation of mean population with imputation in two-phase sampling. Imputation method is used to estimate the missing data. This paper is a review of the work of Thakur et al. [International Journal of Modern Engineering Research, 2 (2012), 3561-3571]. There are two estimators discussed and each estimator is a biased and unbiased. Variance or MSE minimum o…
This paper discusses the existence of iterative method for obtaining the least squares solution to the system Ax = b that have rank-decient. Since the system Ax = b is inconsistent, then a consistent system Mbx = bb, which is the augmented system associated with Ax = b, is used. Then an iterative method of the form (M + γE)bxi = γEbxi
This final project discusses the redeem value and benefit with Paid-Up method. Paid-Up redeem value and Paid-Up benefit are the evaluation of value received by participants for canceling the insurance policy contract before it expires. The calculation of Paid-Up redeem value and Paid-Up benefit can be solved by determining acquisition cost, adjusted premium, and life annuity using Pareto d…
This final project discusses a forecasting using Autoregressive Integrated Moving Average (ARIMA) model. The forecasting method is used to forecast the number of departure and arrival of domestic passengers, at PT. Angkasa Pura II the Branch Office of Sultan Syarif Kasim II Pekanbaru in 2016. The time series data generally contain trend and seasonal elements. Using R language, this study s…
This final project discusses Zillmer’s reserve in term of life insurance by using Rendleman-Bartter interest rate model. Interest rate model of Rendleman-Bartter is a lognormally distributed equilibrium one factor interest rate model and is expressed by stochastic differential equations that follow the Ito’s process. Interest rate models of Rendleman-Bartter has parameters μ and σ to…
This final project discusses the exponentiated Weibull distribution (EWD) with three parameters. This distribution is a modification of theWeibull distribution. The purpose of this research is to obtain the parameters estimate of the exponentiated Weibull distribution. Estimation method used is the maximum likelihood method. Parameter estimates of exponentiated Weibull distribution is used…
This final project discusses parameters of Weibull distribution type-I censored. The estimators are obtained through maximum likelihood method. The estimators of Weibull distribution type-I censored does not have explisit form. Then the numerical approach is applied, which is called approximate maximum likelihood estimators through numerical method, so that the estimators are obtained expl…
This final project discusses a new iterative method obtained by combining Jarratt and Newton method. Analytically it is showed that the method has eight order convergence and its efficiency index is 1.515. Computational results support the analytic result. Furthermore, the computational results show that the proposed method converges faster in obtaining a simple root of the nonlinear equat…
This final project discusses the optimal solution in inventory of a warehouse where the demand and the lead time are uncertain. Determination of the optimal solution is to apply the theory of probabilistic inventory and Monte Carlo simulation. The optimal solution is obtained from Monte Carlo simulation. Keywords: Probabilistic inventory theory, random numbers, Monte Carlo simulation
This nal project discusses the annual premium reserves of healthy insurance of the Burr distribution. The annual premium reserves of healthy insurance calculation is solved by prior determination of the life annuity term, single premium, annual premium. In determining life annuity term is solved by the life chances using Burr distribution. Keywords: Health insurance, premium reserves, Bur…
This nal project discusses an application of the homotopy analysis method to solve a nonlinear Fredholm integral equation of a second kind in the form Urysohn. Then the method is applied to three examples. The results show that the convergence of the homotopy analysis method to the exact solutions is very fast. Keywords: Homotopy analysis method, nonlinear Fredholm integral equation, Ury…
This final project discusses an optimized derivative-free of the Potra-Pt´ak method to solve a nonlinear equation. Analytically, it is shown that the method has the convergence of order four and for each iteration it requires three function evaluations. Furthermore, the computational test shows that the discussed method is superior in terms of the number of iterations needed to obtain an …
This nal project discusses the Holt method and Brown method for forecasting models. Both of these models are used to predict the amount of foreign tou- rist arrivals in Bali in 2015 by taking account the trend factor from time series spanned data. Then a comparison is carried out for both forecasting models to select the better forecasting model with minimum mean absolute percentage error…
Heavy metals in the water might be accumulated in the sediments as well in the aquatic organisms such as crab. The purpose of this research is to understand the Pb and Zn content in the water, sediment and in the mangrove crab (Scylla serrata) present in the waters of Kuala Enok estuary. This research was conducted in March 2017. There were 3 stations, in the cruise line (St 1), in the area wit…
There are illegal logging and domestic activities conducted around the Teluk Buo mangrove forest and thus pollutant originated from those activities reducing the water quality in general. The presence of pollutant affects the mangrove ecosystem as well as the associated organisms, including crabs. To understand the community structure of crabs in the mangrove ecosystem, a research was conducted…
Nygaard Index can be used to determine the trophic state of waters. Calculation of this index is based on the number of phytoplankton species in these following groups, namely Desmidiaceae, Myxophyceae, Chlorococcales, Centric diatom, Pennate diatom and Euglenophyceae. To understand the trophic state of the Lubuk Siam lake, a research has been conducted in February - March 2017. There were thre…