Estimating the Cost of Car Warranty in Indonesia using the Gertsbakh-Kordonsky Method

2020 ◽  
Vol 2 (1) ◽  
pp. 33-40
Author(s):  
Anggis Sagitarisman ◽  
Aceng Komarudin Mutaqin
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Type A ◽  
Claim Data ◽  
Likelihood Method ◽  
Selling Price ◽  
One Dimensional ◽  
Warranty Period ◽  
Kolmogorov Smirnov ◽  
Warranty Costs

AbstractCar manufacturers in Indonesia need to determine reasonable warranty costs that do not burden companies or consumers. Several statistical approaches have been developed to analyze warranty costs. One of them is the Gertsbakh-Kordonsky method which reduces the two-dimensional warranty problem to one dimensional. In this research, we apply the Gertsbakh-Kordonsky method to estimate the warranty cost for car type A in XYZ company. The one-dimensional data will be tested using the Kolmogorov-Smirnov to determine its distribution and the parameter of distribution will be estimated using the maximum likelihood method. There are three approaches to estimate the parameter of the distribution. The difference between these three approaches is in the calculation of mileage for units that do not claim within the warranty period. In the application, we use claim data for the car type A. The data exploration indicates the failure of car type A is mostly due to the age of the vehicle. The Kolmogorov-Smirnov shows that the most appropriate distribution for the claim data is the three-parameter Weibull. Meanwhile, the estimated using the Gertsbakh-Kordonsky method shows that the warranty costs for car type A are around 3.54% from the selling price of this car unit without warranty i.e. around Rp. 4,248,000 per unit.Keywords: warranty costs; the Gertsbakh-Kordonsky method; maximum likelihood estimation; Kolmogorov-Smirnov test.                                   AbstrakPerusahaan produsen mobil di Indonesia perlu menentukan biaya garansi yang bersifat wajar tidak memberatkan perusahaan maupun konsumen. Beberapa pendekatan statistik telah dikembangkan untuk menganalisis biaya garansi. Salah satunya adalah metode Gertsbakh-Kordonsky yang mereduksi masalah garansi dua dimensi menjadi satu dimensi. Pada penelitian ini, metode Gertsbakh-Kordonsky akan digunakan untuk mengestimasi biaya garansi untuk mobil tipe A pada perusahaan XYZ. Data satu dimensi hasil reduksi diuji kecocokan distribusinya menggunakan uji kecocokan Kolmogorov-Smirnov dan taksiran parameter distribusinya menggunakan metode penaksir kemungkinan maksimum. Ada tiga pendekatan yang digunakan untuk menaksir parameter distribusi. Perbedaan dari ketiga pendekatan tersebut terletak pada perhitungan jarak tempuh untuk unit yang tidak melakukan klaim dalam periode garansi. Sebagai bahan aplikasi, kami menggunakan data klaim unit mobil tipe A. Hasil eksplorasi data menunjukkan bahwa kegagalan mobil tipe A lebih banyak disebabkan karena faktor usia kendaraan. Hasil uji kecocokan distribusi untuk data hasil reduksi menunjukkan bahwa distribusi yang cocok adalah distribusi Weibull 3-parameter. Sementara itu, hasil perhitungan taksiran biaya garansi menunjukan bahwa taksiran biaya garansi untuk unit mobil tipe A sekitar 3,54% dari harga jual unit mobil tipe A tanpa garansi, atau sekitar Rp. 4.248.000,- per unit.Kata Kunci: biaya garansi; metode Gertsbakh-Kordonsky; penaksiran kemungkinan maksimum; uji Kolmogorov-Smirnov.

Algebraic solutions in determining the coordinates of the radiator by the results of multi-position measurements of field strength

2021 ◽  
Author(s):  
V.A. Ufaev
Keyword(s):  
Maximum Likelihood ◽  
Field Strength ◽  
Reference Point ◽  
Linear Equations ◽  
Type System ◽  
Energy Parameter ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Algebraic Solution ◽  
Algebraic Solutions

On the basis of the hypothesis of equality of the measured and true values of the amplitude of the field strength, an algebraic solution for estimating the unknown coordinates and the energy parameter of the radiator is obtained. Initially, by compiling and solving a redefined system of linear equations by pseudo-rotation of matrices, the coordinates of the emitter are determined under the assumption of independence of the distance to the reference point from the coordinates of the emitter. Then make and solve the square equation concerning distance to a reference point with the subsequent estimation of coordinates and an energy parameter. The ambiguity of the algebraic solution is resolved by comparing the maximum likelihood functional and choosing the parameters at which its maximum is reached. According to the simulation of a cellular-type system in multiplicative noise, the results of algebraic solutions by the maximum likelihood method and the calculated ones are close, except for a special zone where anomalous changes occur due to the limitations of the coordinate determination method. Algebraic solutions for maximum likelihood estimation provide an increase in the calculation speed of about 500 times. The proposed principle can be used in solving the ambiguity of algebraic solutions in systems of difference-rangefinder type and in the inverse problem of self-positioning of the receiving point by the amplitude of the electromagnetic field of beacons with a known location. The article contains 4 figures, a list of references from 9 sources.

Parameter Estimation of Weibull Distribution Model Based on Ant Colony Algorithm

2014 ◽  
Vol 1070-1072 ◽  
pp. 2073-2078
Author(s):  
Xiu Ji ◽  
Hui Wang ◽  
Chuan Qi Zhao ◽  
Xu Ting Yan
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Ant Colony Algorithm ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Ant Colony ◽  
Likelihood Method ◽  
Distribution Model ◽  
Algorithm Theory

It is difficult to estimate the parameters of Weibull distribution model using maximum likelihood estimation based on particle swarm optimization (PSO) theory for which is easy to fall into premature and needs more variables, ant colony algorithm theory was introduced into maximum likelihood method, and a parameter estimation method based on ant colony algorithm theory was proposed, an example was simulated to verify the feasibility and effectiveness of this method by comparing with ant colony algorithm and PSO.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050005
Author(s):  
Muhammad Mansoor ◽  
M. H. Tahir ◽  
Aymaan Alzaatreh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

scholarly journals Maximum Likelihood Estimation for Three-Parameter Weibull Distribution Using Evolutionary Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Fan Yang ◽  
Hu Ren ◽  
Zhili Hu
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Evolutionary Strategy ◽  
Likelihood Method ◽  
Conventional Algorithm

The maximum likelihood estimation is a widely used approach to the parameter estimation. However, the conventional algorithm makes the estimation procedure of three-parameter Weibull distribution difficult. Therefore, this paper proposes an evolutionary strategy to explore the good solutions based on the maximum likelihood method. The maximizing process of likelihood function is converted to an optimization problem. The evolutionary algorithm is employed to obtain the optimal parameters for the likelihood function. Examples are presented to demonstrate the proposed method. The results show that the proposed method is suitable for the parameter estimation of the three-parameter Weibull distribution.

scholarly journals Bayesian and Maximum Likelihood Estimation for the Weibull Generalized Exponential Distribution Parameters Using Progressive Censoring Schemes

2018 ◽  
pp. 853-868 ◽  
Author(s):  
Ehab Mohamed Almetwally ◽  
Hisham Mohamed Almongy ◽  
Amaal El sayed Mubarak
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Generalized Exponential Distribution ◽  
Progressive Censoring ◽  
Linex Loss ◽  
Distribution Parameters ◽  
Optimal Censoring

In this paper we consider the estimation of the Weibull Generalized Exponential Distribution (WGED) Parameters with Progressive Censoring Schemes. In order to obtain the optimal censoring scheme for WGED, more than one method of estimation was used to reach a better scheme with the best method of estimation. The maximum likelihood method and the method of Bayesian estimation for (square error and Linex) loss function have been used. Monte carlo simulation is used for comparison between the two methods of estimation under censoring schemes. To show how the schemes work in practice; we analyze a strength data for single carbon fibers as a case of real data.

scholarly journals Using Iterative Reweighting Algorithm and Genetic Algorithm to Calculate The Estimation of The Parameters Of The Maximum Likelihood of The Skew Normal Distribution

2021 ◽  
Vol 27 (127) ◽  
pp. 253-264
Author(s):  
مرتضى علاء الخفاجي ◽  
رباب عبد الرضا البكري
Keyword(s):  
Genetic Algorithm ◽  
Maximum Likelihood ◽  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Skew Normal Distribution ◽  
Iterative Reweighting ◽  
Non Linear Equation ◽  
Skew Normal

Excessive skewness which occurs sometimes in the data is represented as an obstacle against normal distribution. So, recent studies have witnessed activity in studying the skew-normal distribution (SND) that matches the skewness data which is regarded as a special case of the normal distribution with additional skewness parameter (α), which gives more flexibility to the normal distribution. When estimating the parameters of (SND), we face the problem of the non-linear equation and by using the method of Maximum Likelihood estimation (ML) their solutions will be inaccurate and unreliable. To solve this problem, two methods can be used that are: the genetic algorithm (GA) and the iterative reweighting algorithm (IR) based on the Maximum Likelihood method. Monte Carlo simulation was used with different skewness levels and sample sizes, and the superiority of the results was compared. It was concluded that (SND) model estimation using (GA) is the best when the samples sizes are small and medium, while large samples indicate that the (IR) algorithm is the best. The study was also done using real data to find the parameter estimation and a comparison between the superiority of the results based on (AIC, BIC, Mse and Def) criteria.

scholarly journals MAXIMUM LIKELIHOOD ESTIMATION OF THE NUMBER OF NUCLEOTIDE SUBSTITUTIONS FROM RESTRICTION SITES DATA

Genetics ◽  
1983 ◽  
Vol 105 (1) ◽  
pp. 207-217
Author(s):  
Masatoshi Nei ◽  
Fumio Tajima
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Iteration Method ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Restriction Enzymes ◽  
Likelihood Method ◽  
Nucleotide Substitutions ◽  
Simple Method ◽  
Restriction Sites

ABSTRACT A simple method of the maximum likelihood estimation of the number of nucleotide substitutions is presented for the case where restriction sites data from many different restriction enzymes are available. An iteration method, based on nucleotide counting, is also developed. This method is simpler than the maximum likelihood method but gives the same estimate. A formula for computing the variance of a maximum likelihood estimate is also presented.

scholarly journals Maximum likelihood estimation of species trees from gene trees in the presence of ancestral population structure

2019 ◽  
Author(s):  
Hillary Koch ◽  
Michael DeGiorgio
Keyword(s):  
Population Structure ◽  
Maximum Likelihood ◽  
Gene Tree ◽  
Likelihood Estimation ◽  
Ease Of Use ◽  
Likelihood Method ◽  
Ancestral Population ◽  
Gene Trees ◽  
Species Trees ◽  
Open Source Software Package

AbstractThough large multilocus genomic datasets have led to overall improvements in phylogenetic inference, they have posed the new challenge of addressing conflicting signals across the genome. In particular, ancestral population structure, which has been uncovered in a number of diverse species, can skew gene tree frequencies, thereby hindering the performance of species tree estimators. Here we develop a novel maximum likelihood method, termed TASTI, that can infer phylogenies under such scenarios, and find that it has increasing accuracy with increasing numbers of input gene trees, contrasting with the relatively poor performances of methods not tailored for ancestral structure. Moreover, we propose a supertree approach that allows TASTI to scale computationally with increasing numbers of input taxa. We use genetic simulations to assess TASTI’s performance in the four-taxon setting, and demonstrate the application of TASTI on a six-species Afrotropical mosquito dataset. Finally, we have implemented TASTI in an open-source software package for ease of use by the scientific community.

scholarly journals New Extension of Weibull Distribution: Copula, Mathematical Properties and Data Modeling

2020 ◽  
Vol 8 (4) ◽  
pp. 972-993
Author(s):  
Hanaa Elgohari ◽  
Haitham Yousof
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Model Parameters ◽  
Graphical Simulation ◽  
Mathematical Properties ◽  
Exponentiated Weibull ◽  
Lifetime Model ◽  
Simulation Results

This paper introduces a new flexible four-parameter lifetime model. Various of its structural properties are derived. The new density is expressed as a linear mixture of well-known exponentiated Weibull density. The maximum likelihood method is used to estimate the model parameters. Graphical simulation results to assess the performance of the maximum likelihood estimation are performed. We proved empirically the importance and flexibility of the new model in modeling four various types of data.

RESILIENCE AND CRITICAL STOCK SIZE IN A STOCHASTIC RECRUITMENT MODEL

2001 ◽  
Vol 09 (01) ◽  
pp. 1-12 ◽  
Author(s):  
JOHAN GRASMAN ◽  
MARK J. HUISKES
Keyword(s):  
Maximum Likelihood ◽  
Stochastic Model ◽  
Stock Assessment ◽  
Life Stage ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Early Life Stage ◽  
Likelihood Method ◽  
Fish Stock ◽  
Stock Size

A stochastic model for fish recruitment is fitted to data after performing an age-structured stock assessment. The main aim is to investigate the relation between safe levels of spawning stock size and fish stock resilience. Resilience indicators, such as stock recovery time and the frequency that a stock is below a critical size, are computed by means of simulation using the fitted stochastic model. The stochastic element of the model describes the early life stage survival of the fish using a nonlinear stochastic Leslie type of matrix. From catch data and fishing mortality rates, the free parameters in the model are estimated by means of a maximum likelihood method. The performance of the maximum likelihood estimation method is tested by means of simulation. The method is applied to data of a halibut population (Hippoglossus stenolepis) in the Southeastern Bering Sea. It turns out that given the fluctuation in recruitment, data of at least 25 consecutive years are required.

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