New wrapped distribution via Richard link function

2017 ◽  
Author(s):  
Arzu Ekinci Demirelli ◽  
Mehmet Gürcan
Keyword(s):  
Link Function ◽  
Wrapped Distribution

scholarly journals Some important details on Richard growth model

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1901-1908
Author(s):  
Mehmet Gurcan ◽  
Arzu Demirelli
Keyword(s):  
Experimental Data ◽  
Growth Models ◽  
Theoretical Distribution ◽  
Applied Statistics ◽  
Link Function ◽  
Parametric Methods ◽  
Location Parameters ◽  
High Flexibility ◽  
Two Parameters ◽  
Wrapped Distribution

The distribution of the data is very important in all of the parametric methods used in the applied statistics. More clearly, if the experimental data fit well to the theoretical distribution, the results will be more efficient in parametric methods. The adaptability of experimental data to a theoretical distribution depends on the flexibility of the theoretical distribution used. If the flexibility of the theoretical distribution is sufficient, it can be used easily for experimental data. Most of the theoretical distributions have shape and location parameters. However, these two parameters are not always sufficient for the distribution adapt to the experimental data. Therefore, theoretical distributions with high flexibility in parametric methods are needed. Obtaining the new theoretical distributions that provide this feature is important for the literature. In this study, a new probability distribution has been obtained via Richard link function which has been high flexibility. In the introduction, important information is given related to growth models and Richard growth curve. Later, some details about the Richard distribution and wrapped distribution have been given.

scholarly journals Testing the Validity of a Link Function Assumption in Repeated Type-II Censored General Step-Stress Experiments

Sankhya B ◽  
2021 ◽  
Author(s):  
Stefan Bedbur ◽  
Thomas Seiche
Keyword(s):  
Null Hypothesis ◽  
Statistical Tests ◽  
Operating Conditions ◽  
Link Function ◽  
Asymptotic Results ◽  
Failure Data ◽  
Stress Levels ◽  
Log Linear ◽  
Multiple Samples ◽  
General Step

AbstractIn step-stress experiments, test units are successively exposed to higher usually increasing levels of stress to cause earlier failures and to shorten the duration of the experiment. When parameters are associated with the stress levels, one problem is to estimate the parameter corresponding to normal operating conditions based on failure data obtained under higher stress levels. For this purpose, a link function connecting parameters and stress levels is usually assumed, the validity of which is often at the discretion of the experimenter. In a general step-stress model based on multiple samples of sequential order statistics, we provide exact statistical tests to decide whether the assumption of some link function is adequate. The null hypothesis of a proportional, linear, power or log-linear link function is considered in detail, and associated inferential results are stated. In any case, except for the linear link function, the test statistics derived are shown to have only one distribution under the null hypothesis, which simplifies the computation of (exact) critical values. Asymptotic results are addressed, and a power study is performed for testing on a log-linear link function. Some improvements of the tests in terms of power are discussed.

scholarly journals Nonparametric estimation of an additive model with a link function

2004 ◽  
Vol 32 (6) ◽  
pp. 2412-2443 ◽  
Author(s):  
Joel L. Horowitz ◽  
Enno Mammen
Keyword(s):  
Nonparametric Estimation ◽  
Additive Model ◽  
Link Function

scholarly journals A Flexible Skewed Link Model for Ordinal Outcomes: An Application to Infertility

2020 ◽  
Vol 8 (A) ◽  
pp. 119-124
Author(s):  
Mohammad Chehrazi ◽  
Seyed Hassan Saadat ◽  
Mahmoud Hajiahmadi ◽  
Mirko Spiroski
Keyword(s):  
Monte Carlo ◽  
Ordinal Data ◽  
Monte Carlo Algorithm ◽  
Link Function ◽  
Posterior Distributions ◽  
Response Data ◽  
Improper Priors ◽  
Ordinal Regression Model ◽  
Link Model ◽  
Categorical Response

BACKGROUND: An important issue in modeling categorical response data is the choice of the links. The commonly used complementary log-log link is inclined to link misspecification due to its positive and fixed skewness parameter. AIM: The objective of this paper is to introduce a flexible skewed link function for modeling ordinal data with some covariates. METHODS: We introduce a flexible skewed link model for the cumulative ordinal regression model based on Chen model. RESULTS: The main advantage suggested by the proposed links is the skewed link provide much more identifiable than the existing skewed links. The propriety of posterior distributions under proper and improper priors is explored in detail. An efficient Markov chain Monte Carlo algorithm is developed for sampling from the posterior distribution. CONCLUSION: The proposed methodology is motivated and illustrated by ovary hyperstimulation syndrome data.

scholarly journals Modelling asthma cases by count analysis approach: Poisson INGARCH and Negative Binomial INGARCH

MATEMATIKA ◽  
2020 ◽  
Vol 36 (1) ◽  
pp. 15-30
Author(s):  
'Aaishah Radziah Jamaludin ◽  
Fadhilah Yusof ◽  
Suhartono Suhartono
Keyword(s):  
Negative Binomial ◽  
Integral Transform ◽  
Rapid Development ◽  
Information Criterion ◽  
Analysis Approach ◽  
Model Assessment ◽  
Link Function ◽  
Estimation Model ◽  
Pearson Residuals ◽  
Log Likelihood

Johor Bahru with its rapid development where pollution is an issue that needs to be considered because it has contributed to the number of asthma cases in this area. Therefore, the goal of this study is to investigate the behaviour of asthma disease in Johor Bahru by count analysis approach namely; Poisson Integer Generalized Autoregressive Conditional Heteroscedasticity (Poisson-INGARCH) and Negative Binomial INGARCH (NB-INGARCH) with identity and log link function. Intervention analysis was conducted since the outbreak in the asthma data for the period of July 2012 to July 2013. This occurs perhaps due to the extremely bad haze in Johor Bahru from Indonesian fires. The estimation of the parameter will be done by quasi-maximum likelihood estimation. Model assessment was evaluated from the Pearson residuals, cumulative periodogram, the probability integral transform (PIT) histogram, log-likelihood value, Akaike’s Information Criterion (AIC) and Bayesian information criterion (BIC). Our result shows that NB-INGARCH with identity and log link function is adequate in representing the asthma data with uncorrelated Pearson residuals, higher in log likelihood, the PIT exhibits normality yet the lowest AIC and BIC. However, in terms of forecasting accuracy, NB-INGARCH with identity link function performed better with the smaller RMSE (8.54) for the sample data. Therefore, NB-INGARCH with identity link function can be applied as the prediction model for asthma disease in Johor Bahru. Ideally, this outcome can assist the Department of Health in executing counteractive action and early planning to curb asthma diseases in Johor Bahru.

Full Credibility with Generalized Linear and Mixed Models

2009 ◽  
Vol 39 (1) ◽  
pp. 61-80 ◽  
Author(s):  
José Garrido ◽  
Jun Zhou
Keyword(s):  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Link Function ◽  
Analysis Method ◽  
Risk Class ◽  
Statistical Analysis Method ◽  
Car Insurance ◽  
Insurance Data

AbstractGeneralized linear models (GLMs) are gaining popularity as a statistical analysis method for insurance data. For segmented portfolios, as in car insurance, the question of credibility arises naturally; how many observations are needed in a risk class before the GLM estimators can be considered credible? In this paper we study the limited fluctuations credibility of the GLM estimators as well as in the extended case of generalized linear mixed model (GLMMs). We show how credibility depends on the sample size, the distribution of covariates and the link function. This provides a mechanism to obtain confidence intervals for the GLM and GLMM estimators.

Modeling on-site wastewater treatment system performance fragility to hydroclimate stressors

2016 ◽  
Vol 74 (12) ◽  
pp. 2917-2926 ◽  
Author(s):  
Laura E. Kohler ◽  
JoAnn Silverstein ◽  
Balaji Rajagopalan
Keyword(s):  
Wastewater Treatment ◽  
Generalized Linear Model ◽  
Stream Flow ◽  
Link Function ◽  
Climate Factors ◽  
Related Factors ◽  
Health Records ◽  
Boulder County ◽  
County Public Health ◽  
Wastewater Treatment Systems

Increasing variability of climate-related factors, especially precipitation and temperature, poses special risks to on-site wastewater treatment systems (OWTS), which depend on subsurface saturation conditions for treatment and dispersion of wastewater. We assess OWTS fragility – the degree to which a system loses functionality – as a step to characterizing the resilience of residential wastewater treatment systems. We used the frequency and indexed severity of OWTS failures and resulting repairs to quantify fragility as a function of hydroclimate variables, including precipitation, temperature and stream flow. The frequency of each category of repair (minor, moderate and major) for 225 OWTS obtained from Boulder County public health records was modeled as a function of climate factors using a generalized linear model with a Poisson distribution link function. The results show that prolonged precipitation patterns, with monthly rainfall >10.16 cm, influence OWTS fragility, and complete loss of OWTS functionality, requiring replacement, is impacted by high temperatures, frequency of wetter-than-normal months, and the magnitude of peak stream flow in the watershed. Weather-related covariates explained 70% of the variability in OWTS major repair data between 1979 and 2006. These results indicate that fragility arising from climate factors, and associated costs to owners, environmental and health impacts, should be considered in planning, design and operation of OWTS.

Complete Solutions to Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy With M-Homogenization

1992 ◽  
Author(s):  
Anoop K. Dhingra ◽  
Jyun-Cheng Cheng ◽  
Dilip Kohli
Keyword(s):  
Group Theory ◽  
Matrix Method ◽  
Numerical Results ◽  
Path Generation ◽  
Link Function ◽  
Homotopy Methods ◽  
Motion Generation ◽  
The Matrix ◽  
Function Generators ◽  
Complete Solutions

Abstract This paper presents complete solutions to the function, motion and path generation problems of Watt’s and Stephenson six-link, slider-crank and four-link mechanisms using homotopy methods with m-homogenization. It is shown that using the matrix method for synthesis, applying m-homogeneous group theory, and by defining compatibility equations in addition to the synthesis equations, the number of homotopy paths to be tracked can be drastically reduced. For Watt’s six-link function generators with 6 thru 11 precision positions, the number of homotopy paths to be tracked in obtaining all possible solutions range from 640 to 55,050,240. For Stephenson-II and -III mechanisms these numbers vary from 640 to 412,876,800. For 6, 7 and 8 point slider-crank path generation problems, the number of paths to be tracked are 320, 3840 and 17,920, respectively, whereas for four-link path generators with 6 thru 8 positions these numbers range from 640 to 71,680. It is also shown that for body guidance problems of slider-crank and four-link mechanisms, the number of homotopy paths to be tracked is exactly same as the maximum number of possible solutions given by the Burmester-Ball theories. Numerical results of synthesis of slider-crank path generators for 8 precision positions and six-link Watt and Stephenson-III function generators for 9 prescribed positions are also presented.

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