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…
ABSTRACT This final project discusses the families of Newton-Like methods derived from a combination of the secant method with Newton’s method based on the trapezoidal rule and inverse function to find a root of nonlinear equations. Analytically, it is shown that the iterative methods have the order of convergence four and for each iteration, they require four function evaluations, so t…
ABSTRACT We discusses the existence and uniqueness of the solution, which was obtained using Adomian decomposition method, of a nonlinear quadratic integral equ- ation. The discussion was continued by providing an analytical study of the convergence and the absolute error which are obtained by the solution found using Adomian decomposition method. The process of obtaining the solution of …
ABSTRACT This paper studies three regression ratio estimators for population mean Y of the variable Y using information on two auxiliary variables X dan Z under simple random sampling without replacements. This discussion is a review from the article of Singh et al. [Statistics in Transition 10(1): 85-100]. All estimators are biased. The efficient estimator is the one with the minimum Mean…
ABSTRACT Health insurance is one type of insurance products that specifically guarantees the cost of health insurance or care when participants experience health problems that caused hospitalized. We discuss about the huge of annual premium back up of term health insurance joint life status with using constant force assumption, by first determining the term life annuity, single premium of …
ABSTRACT Partial differential equations have three equations are parabolic, elliptic, and hyperbolik equations. In this article discussed about the correspondence between parabolic and elliptic equations of the heat equations is seen from the flow of heat. u is temperature, if u at the two-dimensional heat equation is not effect by time then the heat flow in stable state and parabolic equt…