New Estimation Method for Mixture of Normal Distributions

2017 ◽  
pp. 217-233
Author(s):  
Qianfang Hu ◽  
Zheng Wei ◽  
Baokun Li ◽  
Tonghui Wang
Keyword(s):  
Estimation Method ◽  
Normal Distributions ◽  
Mixture Of Normal Distributions

scholarly journals Normal approximation for mixtures of normal distributions and the evolution of phenotypic traits

2021 ◽  
Vol 53 (1) ◽  
pp. 162-188
Author(s):  
Krzysztof Bartoszek ◽  
Torkel Erhardsson
Keyword(s):  
Normal Distribution ◽  
Phenotypic Trait ◽  
Phenotypic Traits ◽  
Normal Distributions ◽  
Average Value ◽  
Conditional Moments ◽  
Mixture Of Normal Distributions ◽  
Explicit Bounds ◽  
Mixtures Of Normal Distributions ◽  
Parameter Values

AbstractExplicit bounds are given for the Kolmogorov and Wasserstein distances between a mixture of normal distributions, by which we mean that the conditional distribution given some $\sigma$ -algebra is normal, and a normal distribution with properly chosen parameter values. The bounds depend only on the first two moments of the first two conditional moments given the $\sigma$ -algebra. The proof is based on Stein’s method. As an application, we consider the Yule–Ornstein–Uhlenbeck model, used in the field of phylogenetic comparative methods. We obtain bounds for both distances between the distribution of the average value of a phenotypic trait over n related species, and a normal distribution. The bounds imply and extend earlier limit theorems by Bartoszek and Sagitov.

Using Mixture of Normal Distributions to Detect Treatment Effects when the Frequentist Method Fails

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Anthony Orlando
Keyword(s):  
Dose Response ◽  
Linear Models ◽  
Controlled Trial ◽  
Response To Treatment ◽  
Double Blind ◽  
Underlying Assumption ◽  
Normal Distributions ◽  
Efficacy Measure ◽  
Baseline Weight ◽  
Mixture Of Normal Distributions

Background: Results from a clinical trial can either support the efficacy and safety of a new compound or fail to provide such evidence. One reason for ‘non[1]positive’ result is due to the underlying assumption of normality and homogeneity of variances, which are quite often violated when analyzing data from clinical trials, despite randomization. A question of interest is can we obtain more informative results when using mixture of normal distributions or linear models (MLMs) in such cases. Introduction: MLM can be used when traditional methods fail. MLMs “search” within the variability in data to identify components or subgroups of individuals (also known as latent classes) who have common intercepts and common slopes of change in a variable/endpoint of interest but whose intercepts and slopes are different from other subsets of patients. Thus, MLMs can be used to identify subgroups of patients exhibiting differential response to treatment within each treatment arm. The purpose of our study was to examine the usefulness of using MLM in such circumstances. Methods: Data of 155 subjects taken from a Multicenter, randomized, double blind, placebo controlled trial that evaluated the efficacy of Cpn10, administered twice weekly subcutaneously to treat Rheumatoid Arthritis was taken to evaluate the usefulness of MLM. The primary efficacy measure ACR20 was analyzed using a 3-step process: first, MLM was used to estimate RA duration using a 3-component model. The second step took the results of the first step to inform the logistic model and its analyses. Model was fitted with an intercept, MLM components, treatment arm, RA duration (linear and quadratic), dose response (modeled as an interaction effect), age and baseline weight. LOCF was used to impute for missing data. Data was analyzed using MLM and SAS v 9.0. Results: The model was a good fit to the data with a likelihood ratio significant at p=0.026, and a significant increase in the -2log L. We also observed low p-values for those variables that were non normal. Overall and for the 75 mg dose, Cpn 10 was efficacious relative to placebo, p<0.050. We also observed that dose response was significant at p><0.15 Conclusion: The use of MLM adds value because it can be used to understand the disease experience or the value of treatment when traditional statistical methods cannot. Key words: Mixture of linear models, normality, entropy.

scholarly journals How to Distinguish Languages and Dialects

2020 ◽  
Vol 45 (4) ◽  
pp. 823-831 ◽  
Author(s):  
Søren Wichmann
Keyword(s):  
Temporal Distance ◽  
Strong Tendency ◽  
Data Sets ◽  
Language Group ◽  
Lexical Information ◽  
Normal Distributions ◽  
Mixture Of Normal Distributions ◽  
The Mean ◽  
One To One

The terms “language” and “dialect” are ingrained, but linguists nevertheless tend to agree that it is impossible to apply a non-arbitrary distinction such that two speech varieties can be identified as either distinct languages or two dialects of one and the same language. A database of lexical information for more than 7,500 speech varieties, however, unveils a strong tendency for linguistic distances to be bimodally distributed. For a given language group the linguistic distances pertaining to either cluster can be teased apart, identifying a mixture of normal distributions within the data and then separating them fitting curves and finding the point where they cross. The thresholds identified are remarkably consistent across data sets, qualifying their mean as a universal criterion for distinguishing between language and dialect pairs. The mean of the thresholds identified translates into a temporal distance of around one to one-and-a-half millennia (1,075–1,635 years).

Hedge Funds: The Good, the Bad, and the Lucky

2017 ◽  
Vol 52 (3) ◽  
pp. 1081-1109 ◽  
Author(s):  
Yong Chen ◽  
Michael Cliff ◽  
Haibei Zhao
Keyword(s):  
Hedge Funds ◽  
Expectation Maximization ◽  
Investment Strategy ◽  
Performance Measure ◽  
Cross Sectional ◽  
Normal Distributions ◽  
Out Of Sample ◽  
Mixture Of Normal Distributions ◽  
Skill Groups ◽  
The Mean

We develop an estimation approach based on a modified expectation-maximization (EM) algorithm and a mixture of normal distributions associated with skill groups to assess performance in hedge funds. By allowing luck to affect both skilled and unskilled funds, we estimate the number of skill groups, the fraction of funds from each group, and the mean and variability of skill within each group. For each individual fund, we propose a performance measure combining the fund’s estimated alpha with the cross-sectional distribution of fund skill. In out-of-sample tests, an investment strategy using our performance measure outperforms those using estimated alpha and t-statistic.

scholarly journals One-Sample $t$-Test When Sampling from a Mixture of Normal Distributions

1977 ◽  
Vol 5 (4) ◽  
pp. 803-807 ◽  
Author(s):  
Austin F. S. Lee ◽  
John Gurland
Keyword(s):  
T Test ◽  
Normal Distributions ◽  
Mixture Of Normal Distributions

scholarly journals Probabilistic photovoltaic power forecasting model based on deterministic forecasts

2020 ◽  
Vol 152 ◽  
pp. 01003
Author(s):  
L. Alfredo Fernandez-Jimenez ◽  
Sonia Terreros-Olarte ◽  
Pedro J. Zorzano-Santamaria ◽  
Montserrat Mendoza-Villena ◽  
Eduardo Garcia-Garrido
Keyword(s):  
Genetic Algorithm ◽  
Forecasting Model ◽  
Probabilistic Forecasting ◽  
Deterministic Models ◽  
Conditional Quantile ◽  
Normal Distributions ◽  
Probabilistic Forecasts ◽  
Mixture Of Normal Distributions ◽  
Quantile Regression Method ◽  
Power Forecasting

This paper presents an original probabilistic photovoltaic (PV) power forecasting model for the day-ahead hourly generation in a PV plant. The probabilistic forecasting model is based on 12 deterministic models developed with different techniques. An optimization process, ruled by a genetic algorithm, chooses the forecasts of the deterministic models in order to achieve the probability distribution function (PDF) for the PV generation in each one of the daylight hours of the following day in a parametric approach. The PDFs, which constitute the probabilistic forecasts, are a mixture of normal distributions, each one centred in the forecasts of the selected deterministic models. The genetic algorithm chooses the deterministic forecasts, the variance of the normal distributions and their weights in the mixture. In a case study the proposed model achieves better forecasting results than the obtained with the conditional quantile regression method applied to the same data used to develop the deterministic forecasting models.

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