In this article we study three linear regression ratio estimators for the population mean on simple random. This study is a review of the article of Singh et all [Statistics in Transition-new series, 10: 85-100]. Each estimator is a biased estimator and the is mean square errors are determined. Estimator with the smallest mean square error is the most efficient one. An example is given at t…
Estimators discussed in this paper are three estimators to population ratio using variable transformation i.e estimator of population ratio using dual variable, regression-type estimator of population ratio and ratio-type estimator of population ratio, which is a review from the article of Onyeka et.al [Global Journal of Science Frontier Research 13(2013):57-65]. The three estimators are b…
Estimators discussed here are three estimators for estimating population variance in simple random sampling without replacement, i.e. exponential ratio estimator using variance of auxiliary variable, and exponential ratio and product estimators using mean of auxiliary variable. This work is a review of article written by Asghar et al. [Revista Colombiana de Estadistica, 37 (2014): 213-224].…
We discusses a Newton-type method for multiple roots, which is derived using a linear combination of Newton’s method for multiple roots and an iterative method derived based on a quadrature Gauss-type. Analytic studies show that this iterative method has a third order of convergence and for each iteration, it requires function evaluations three times, so that the efficiency index of the …
This paper study three type of regression ratio estimators for the population mean on simple random sampling using minimum and maximum auxiliary variables. This study is a review from the article of Singh et. al. [Statistics in Transition, 10: 85-100]. Then, the mean square error of this three estimators are compared. Estimator with the smallest mean square error is the most efficient estim…
This paper discusses premium reserve endowment life insurance for years. The reserve is calculated by the method of full preliminary term based on net annual premium, with the first net annual premium and the second net annual premium . Net annual premium is affected by amount of single premium and annuity due. De Moivre law is applied to calculate the reserve. Keywords: modified reserve, …
This paper discusses the preconditioner of Gauss-Seidel method in solving a linear system Ax = b, where A is of the form M-matrix, which is reviewed of Li-ying Sun [Journal of Computational and Applied Mathematics, 181(2005), 336 − 341]. Numerically shown that the spectral radius of the Gauss-Seidel method with preconditioner is smaller than that of the SOR method and Gauss-Seidel method…
This final project discusses three ratio estimators for the population ratio using the coefficient regression and dual, which is a review from the article of Onyeka et.al [Global Journal of Science Frontier Research, 13(2013):57-65]. The three estimators are biased estimators and their mean square error are determined. The mean square error for each estimator is evaluated and compared to ob…
This final project discusses an iterative method obtained through modification of Steffensen’s method using a parameter that depends on divided differences. Analysis of convergence shows that the discussed method has super cubic con- vergence, i.e. 3.383. Computational test shows that the discussed iterative method meets the theoretical study conducted. Numerical comparisons of the discu…
This final project discusses the application of ARCH-GARCH method to calculate value at risk. The application process begins by constructing models using ARCH-GARCH. This model is used to count the variance and the volatility of share price index of LQ 45. This model considers heteroscedasticity factor of time series data used. Based on the volatility, value at risk of share price index of…
This project discusses a new iterative method based on the variational iteration technique, which is free from second derivative. This method has two-step in which the first-step is Newton’s method. In the discussion three specific cases by choosing certain free functions in a general form of the variational iteration technique are mention. Analytically it is shown that the general form o…
This final project discusses some identities of generalized Fibonacci sequence, n u , which satisfies linear homogeneous recurrence relations of order two having a non-zero constant coefficient. Then given some matrices, we show that the npower of these matrices provide some identities for n i i u 0 2 , n n2 u u , and n i i i u u 0 1 . At the end we giv…
This final project discusses the necessary and sufficient condition for the system of linear equations Ax = b where A is an m × n matrix, with m < n and b is an n × 1 vector to have a solution. The discussion involves determining the number of single variables by looking at columns lowering rank and determining the value of the single variables. Keywords: nonhomogeneous system of linear …
This final project discusses the term life insurance premiums using decreasing annuity. The initial annuity payment by n unit of payments and subsequent payments always decrease by one unit of the previous period. Determination of term life insurance premiums with decreasing annuity are based on the Balducci assumption and independent interest rate, which is one model of the time series of…
Option is a contract between option sellers and option buyers. The option seller guarantees the rights of the buyer to buy or to sell a particular stock at time and with price that have been determined. This final project explains the determination of the stock price by the dividen distribution. The model used is Black-Scholes model in the form of partial differential equations. Then in ord…
This final project discusses the modification of Newton’s method using the com- posite trapezoidal rule to approximate an indefinite integral in its derivation. Analytically it is demonstrated that the convergence of Newton’s composite trapezoidal rule is three. Furthermore, computational tests show that the di- scussed method can be used as an alternative method in their class in solvi…
This final project discusses the generalized power mean modification of New- ton’s method to solve nonlinear equations obtained by modifying Newton’s me- thod using a trapezoidal quadrature formula. It is analytically demonstrated that the method has convergence order of three or five. Computational results support the analytical studies. Numerical simulations show that the method is c…
This paper discusses how to obtain the Taylor polynomials solution of a higher order linear differential-difference equation with variable coefficients whose initial conditions are known. The process begins by assuming the solution of a higher order linear differential-difference equation in the form of polynomials Taylor. Then it is followed by presenting this equation and its initial con…
This final project discusses generalization Simpson-Newton method to solve nonlinear equations. The method is derived by replacing the coefficients of Simpson-Newton method with four parameters in which the sum of parameters in the denominator of Simpson-Newton method is the same as the parameter in the numerator of Simpson-Newton method. Analytically, it is shown that the method is of ord…
This final project discusses the Holt-Winters forecasting method that takes into account the effect of Eid. This method is used to predict total domestic passengers departing in 5 major ports in Indonesia. Then a comparison is carried out between the method of Holt-Winters and Holt-Winters method that take into account the effect of Eid. The comparison is done by comparing the mean square …