Many activities in Maninjau Lake contribute the input of organic and anorganic matter that affects the water quality, especially nutrient concentration in waters. A research aims to understand the trophic state of Maninjau Lake based on TSI has been conducted on January to February 2017. There were 4 stations, namely, Station 1 (bay area), Station 2 (inlet area), Station 3 (fish floating cages …
This final project discusses the annual premium whole life insurance on the joint life by using Frank copula distribution and using rate Cox Ingersoll Ross. The calculation of the annual premium is obtained by annuity present value and single premium. Solving the annuity present value and single premium, the survival and curtate future lifetime must be known in advance. Keywords: Life insu…
This final project discusses a modified Newton’s method using a semi-closed quadrature. Analytically it is shown that the method is of order three. Computational tests using five test functions show that the proposed method is better than Newton’s method and Soheili’s Method in terms of the number of iterations needed to get an approximate root. Keywords: Newton method, Soheili metho…
Sago factory in the Tanjung Kulim Village usually flow the sago liquid waste directly to the Asam Strait and thus pollute the waters. A research aims to understand the sago waste water pollution load in the strait has been conducted in April 2017. There were 3 station, namely Station 1 (fresh liquid waste), Station 2 (in the drainage of sago factory) and Station 3 (Asam Strait area). Result sho…
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 …