Using Weibull Distribution for Modeling Bimodal Diffusion Curves: A Naive Framework to Study Product Life Cycle

2019 ◽  
Vol 16 (07) ◽  
pp. 1950050
Author(s):  
Adarsh Anand ◽  
Richie Aggarwal ◽  
Ompal Singh
Keyword(s):  
Weibull Distribution ◽  
Product Life Cycle ◽  
Scale Parameter ◽  
Functional Model ◽  
Real Life ◽  
Step Function ◽  
Unknown Parameters ◽  
Consumer Durables ◽  
Study Product ◽  
Better Than

With the purpose of understanding differing shapes of sales curve (unimodal and bimodal) this paper discusses a naive way for viewing the diffusion process for consumer durables. In this paper, a step functional model involving two-step Weibull distribution with four unknown parameters is characterized wherein the shape of the density function of the models depends upon the shape and scale parameter of Weibull distribution. Empirical analysis on real life sales datasets indicates that the Weibull step function model is more flexible and fits better than the other models.

scholarly journals On the Properties and Applications of a Transmuted Lindley-Exponential Distribution

2019 ◽  
pp. 1-13
Author(s):  
Adamu Abubakar Umar ◽  
Innocent Boyle Eraikhuemen ◽  
Peter Oluwaseun Koleoso ◽  
Jerry Joel ◽  
Terna Godfrey Ieren
Keyword(s):  
Exponential Distribution ◽  
Continuous Distribution ◽  
Real Life ◽  
Likelihood Estimation ◽  
Good Evidence ◽  
Survival Times ◽  
Probability Models ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Better Than

The Quadratic rank transmutation map proposed for introducing skewness and flexibility into probability models with a single parameter known as the transmuted parameter has been used by several authors and is proven to be useful. This article uses this method to add flexibility to the Lindley-Exponential distribution which results to a new continuous distribution called “transmuted Lindley-Exponential distribution”. This paper presents the definition, validation, properties, application and estimation of unknown parameters of the transmuted Lindley-Exponential distribution using the method of maximum likelihood estimation. The new distribution has been applied to a real life dataset on the survival times (in days) of 72 guinea pigs and the result gives good evidence that the transmuted Lindley-Exponential distribution is better than the Lindley-Exponential distribution, Exponential distribution and Lindley distribution based on the dataset used.

scholarly journals Weighted Version of Generalized Inverse Weibull Distribution

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Sofi Mudasir ◽  
S. P. Ahmad
Keyword(s):  
Weibull Distribution ◽  
Generalized Inverse ◽  
Real Life ◽  
Moment Generating Function ◽  
Weighted Version ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Inverse Weibull Distribution ◽  
Better Than

Weighted distributions are used in many fields, such as medicine, ecology, and reliability. A weighted version of the generalized inverse Weibull distribution, known as weighted generalized inverse Weibull distribution (WGIWD), is proposed. Basic properties including mode, moments, moment generating function, skewness, kurtosis, and Shannon’s entropy are studied. The usefulness of the new model was demonstrated by applying it to a real-life data set. The WGIWD fits better than its submodels, such as length biased generalized inverse Weibull (LGIW), generalized inverse Weibull (GIW), inverse Weibull (IW) and inverse exponential (IE) distributions.

THE IMPACTS OF INDIVIDUAL INFORMATION ON LOSS RESERVING

2020 ◽  
pp. 1-45
Author(s):  
Zhigao Wang ◽  
Xianyi Wu ◽  
Chunjuan Qiu
Keyword(s):  
Information Model ◽  
Statistical Properties ◽  
Unknown Parameters ◽  
Asymptotic Behaviors ◽  
Computation Procedure ◽  
General Insurance ◽  
Loss Reserving ◽  
Portfolio Size ◽  
Better Than ◽  
Individual Information

Abstract The projection of outstanding liabilities caused by incurred losses or claims has played a fundamental role in general insurance operations. Loss reserving methods based on individual losses generally perform better than those based on aggregate losses. This study uses a parametric individual information model taking not only individual losses but also individual information such as age, gender, and so on from policies themselves into account. Based on this model, this study proposes a computation procedure for the projection of the outstanding liabilities, discusses the estimation and statistical properties of the unknown parameters, and explores the asymptotic behaviors of the resulting loss reserving as the portfolio size approaching infinity. Most importantly, this study demonstrates the benefits of individual information on loss reserving. Remarkably, the accuracy gained from individual information is much greater than that from considering individual losses. Therefore, it is highly recommended to use individual information in loss reserving in general insurance.

scholarly journals CAD integrated automatic recognition of weld paths

2021 ◽  
Author(s):  
Tuan Anh Tran ◽  
Andrei Lobov ◽  
Tord Hansen Kaasa ◽  
Morten Bjelland ◽  
Ole Terje Midling
Keyword(s):  
Life Cycle ◽  
Spatial Analysis ◽  
Product Life Cycle ◽  
Real Life ◽  
Automatic Recognition ◽  
Integrated Method ◽  
Weld Joints ◽  
Related Information ◽  
Almost All ◽  
Sequential Assembly

AbstractIn this paper, a CAD integrated method is proposed for automatic recognition of potential weld locations in large assembly structures predominantly comprised of weld joints. The intention is to reduce the total man-hours spent on manually locating, assigning, and maintaining weld-related information throughout the product life cycle. The method utilizes spatial analysis of extracted stereolithographic data in combination with available CAD functions to determine whether the accessibility surrounding a given intersection edge is sufficient for welding. To demonstrate the method, a system is developed in Siemens NX using their NXOpen Python API. The paper presents the application of the method to real-life use cases in varying complexity in cooperation with industrial partners. The system is able to correctly recognize almost all weld lines for the parts considered within a few minutes. Some exceptions are known for particular intersection lines located deep within notched joints and geometries weldable through sequential assembly, which are left as a subject to further works.

scholarly journals Empirical Stochastic Model of Multi-GNSS Measurements

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4566
Author(s):  
Dominik Prochniewicz ◽  
Kinga Wezka ◽  
Joanna Kozuchowska
Keyword(s):  
Stochastic Model ◽  
Density Ratio ◽  
Functional Model ◽  
Optimal Solution ◽  
Global Navigation Satellite Systems ◽  
Unknown Parameters ◽  
Short Baseline ◽  
Stochastic Parameters ◽  
Dependent Model ◽  
The Impact

The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

scholarly journals An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

OR Spectrum ◽  
2021 ◽  
Author(s):  
Adejuyigbe O. Fajemisin ◽  
Laura Climent ◽  
Steven D. Prestwich
Keyword(s):  
Real Life ◽  
Forest Harvesting ◽  
Cutting Stock Problem ◽  
Cutting Stock ◽  
Decomposition Approach ◽  
New Class ◽  
Bilevel Problem ◽  
Programming Techniques ◽  
Bilevel Problems ◽  
Better Than

AbstractThis paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approach.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family

2019 ◽  
Vol 12 (4) ◽  
pp. 171
Author(s):  
Ashis SenGupta ◽  
Moumita Roy
Keyword(s):  
Entire Range ◽  
Goodness Of Fit ◽  
Stable Distribution ◽  
Real Life ◽  
Circular Statistics ◽  
Directional Statistics ◽  
Symmetric Stable Distribution ◽  
Stable Family ◽  
Family Of Distributions ◽  
Better Than

The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter α lies between 1 and 2. A similar approach can be adopted when α (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.

scholarly journals Elimination of some unknown parameters and its effect on outlier detection

2012 ◽  
Vol 18 (3) ◽  
pp. 347-362 ◽  
Author(s):  
Serif Hekimoglu ◽  
Bahattin Erdogan ◽  
Nursu Tunalioglu
Keyword(s):  
Outlier Detection ◽  
Functional Model ◽  
Computational Time ◽  
Control Network ◽  
Unknown Parameters ◽  
Reliable Estimation ◽  
Cofactor Matrix ◽  
Simulation Results ◽  
Horizontal Control

Outliers in observation set badly affect all the estimated unknown parameters and residuals, that is because outlier detection has a great importance for reliable estimation results. Tests for outliers (e.g. Baarda's and Pope's tests) are frequently used to detect outliers in geodetic applications. In order to reduce the computational time, sometimes elimination of some unknown parameters, which are not of interest, is performed. In this case, although the estimated unknown parameters and residuals do not change, the cofactor matrix of the residuals and the redundancies of the observations change. In this study, the effects of the elimination of the unknown parameters on tests for outliers have been investigated. We have proved that the redundancies in initial functional model (IFM) are smaller than the ones in reduced functional model (RFM) where elimination is performed. To show this situation, a horizontal control network was simulated and then many experiences were performed. According to simulation results, tests for outlier in IFM are more reliable than the ones in RFM.

scholarly journals GM(1,1;λ) with Constrained Linear Least Squares

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Model Fitting ◽  
Ordinary Least Squares ◽  
Linear Least Squares ◽  
Unknown Parameters ◽  
Constrained Problems ◽  
Linear Least Squares Problems ◽  
Ordinary Least Squares Method ◽  
Better Than

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

Sign in / Sign up

Export Citation Format

Share Document