ABSTRACT This nal project discusses the properties sum of the reciprocal Fibonacci numbers with two or three functions of sums of the reciprocal Fibonacci numbers, and discusses the sum of the reciprocal Fibonacci numbers using the oor function with mn Fibonacci numbers for any value of m and n which are even and odd integers. The sum is proven by using the denition and properties of …
In this project, we discuss the modification of Newton’s method, which is a Predictor and Corrector method, to solve a nonlinear equation. Using a series based on the equation error of the method, we show that the order of convergence of the method is 1 + p2 and for each iteration, it requires two function evaluations, so the efficiency index of the method is 2.4142. To see the advantage…
This thesis discusses a derivative free three-step iterative method to solve a nonlinear equation. The proposed method is derived by estimating the first de-rivative of the method proposed by Sharma and Arora [Appl. Math. Comput., 273 (2016), 924-933] using a divided difference by one parameter. Analytically it is shows that the method has an eighth order convergence and requires four function…
The proposes of this research are to improve the learning process and to increase mathematics achievement from the students with applied problem based learning model. Class action research is carried out in two cycles. First cycles has three meetings and one daily tests, second cycles has three meetings and one daily tests. The research subject is the students of class VII9 SMP Negeri 21 Pekanb…
The final project discusses a new method to solve transportation called max-min total opportunity cost, where the proposed method is easy since computation works. Northwest corner method, least cost method and Vogel’s approxima- tion method use to determine the basic feasible solution, and to compare with the new method. Then simplex transportation method is used to verify the optimality…
This paper discusses the stability analysis of the population in Lotka-Volterra model of the three species. The analysis was conducted on the stability of the equilibrium point and the coordinate plane through linear analysis. Fur- thermore, some numerical examples show that the solutions obtained using the parameter values provide an overview of the development of the three species. Key w…
In this final project, we discuss the derivation of an optimal iterative method using a quadratic polynomial, which is a review and a correction of a part of Fern´andez-Torres and V´asquez-Aquino’s article [Advances in Numerical Ana- lysis, 10: 1-8, 2013]. Analytically we show that the obtained method has an order of convergence four and requires three function evaluations per iteration…
This final project discusses a new family of three-step iteration method. Analytically, it is showed using Taylor expansion and geometry series that this iterative method has a convergence eight-order. Numerical comparisons show that this method is comparable with the others eight-order methods and can be used as an alternative method in solving nonlinear equations. Keywords: Iterative met…
ABSTRACT This paper discusses the probability of the state when surplus become negative at the first time in the insurance, that is called the probability of ruin, for the claim amount is supposed to be a combination of exponential distribution. We assume that the claim number distribution is Poisson and the waiting time distribution of the claim is exponential. In this paper, we determine…
ABSTRACT This script discusses the accumulated value of the immediate annuity for m times per year. The assumption of uniform distribution is used in determining the accumulated value of the immediate annuity, which is a linear approximation to the probability that the insurance participant died. The accumulated value of the annuity is influenced by cash value annuity paid by insurance par…
ABSTRACT We discuss an inventory control with shortage affected by discount and inflation. The optimal level of inventory is determined by establishing the discount, and also by establishing the ordering interval. The discount can increase savings when inflation occured. An numerical example is given at the end of discussion. Keywords: shortage, discount, inflation rate
ABSTRACT This final project discusses three estimators for the population mean in simple random sampling are dual ratio estimator, dual product estimator and dual ratiocum- product estimator. These estimators are biased estimators. The mean square error for each estimator is evaluated and compared to obtain the most efficient one. This comparison shows that the dual ratio-cum-product estim…
ABSTRACT We discuss about two ratio estimators in stratified adaptive cluster random sampling are ratio estimator for population mean and ratio estimator proposed by Hansen-Hurwitz. The second estimator is biased. The next will be determined Mean Square Error of each estimator. So Mean Square Error of the two estimator will be compared to obtain an efficient ratio estimator. Keywords: rat…
ABSTRACT Product estimators of the population mean in simple random sampling and ranked set sampling that suggested are two product estimators using the auxiliary variable quartiles given by Al-Omari [International Journal of Human and Social Sciences., 4 (2009), pp. 1181-1185]. These estimators are biased estimators, so that the Mean Square Error is calculated for each estimators to obtai…
ABSTRACT This paper discusses the estimators of regression cum-ratio proposed by Yan and Tian [6] for the population mean. These three estimators use the auxiliary variable of the coefficients of kurtosis and skewness in simple random sampling. All estimators are biased estimators. The most efficient estimator is the estimator that has the smallest mean square error obtained by comparing t…
ABSTRACT This script discusses the calculation of the prospective reserve of an endowment life insurance with uniform assumption for individual life status. The uniform assumption is an assumption that takes the uniform distribution for the probability density function, hence it can be used in a reserve premium calculation. The reserve premium available in life insurance company is influen…
ABSTRACT In this paper we study the ratio estimator, product estimator and combination of ratio estimator and product estimator in systematic random sampling, which is a review and an expansion correction from the article of Singh, et. al. [Journal of Modern Applied Statistical Methods, 10: 424-435]. Each estimator is a biased estimator and the mean square errors are determined. Estimator …
ABSTRACT This final project discusses a technique to estimate an error in numerical integration methods, which is a review and an expansion, as well as partial correction from the article Peter R. Mercer [The College Mathematics Journal, 36 (2005): 27-34]. After obtaining the error estimates of the numerical integration methods for a single interval, composite error estimate forms are deve…
ABSTRACT This paper discusses the efficient sampling methods to ranked set sampling, extreme ranked set sampling, and median ranked set sampling for simple linear regression estimators whose population mean known with concomitant variable. Their relative efficiency have been compared in order to find the most efficient estimator. Key words: extreme ranked set sampling, median ranked set sa…
ABSTRACT This final project discusses about prospective reserve of premium last survivor endowment insurance. Last survivor status is life insurance of two persons who are and years old with a certain that premium payed until the last death of insurance clients. The calculation of prospective reserve of last survivor endowment is done by previously determining the present value annuity, th…