Interval estimation for the mean of lognormal data with excess zeros

2013 ◽  
Vol 83 (11) ◽  
pp. 2447-2453 ◽  
Author(s):  
Xinmin Li ◽  
Xiaohua Zhou ◽  
Lili Tian
Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3272
Author(s):  
Xiao Wang ◽  
Xinmin Li

This paper considers interval estimations for the mean of Pareto distribution with excess zeros. Three approaches for interval estimation are proposed based on fiducial generalized pivotal quantities (FGPQs), respectively. Simulation studies are performed to assess the performance of the proposed methods, along with three measurements to determine comparisons with competing approaches. The advantages and disadvantages of each method are provided. The methods are illustrated using a real phone call dataset.


Parasitology ◽  
2009 ◽  
Vol 136 (13) ◽  
pp. 1695-1705 ◽  
Author(s):  
P. VOUNATSOU ◽  
G. RASO ◽  
M. TANNER ◽  
E. K. N'GORAN ◽  
J. UTZINGER

SUMMARYProgress has been made in mapping and predicting the risk of schistosomiasis using Bayesian geostatistical inference. Applications primarily focused on risk profiling of prevalence rather than infection intensity, although the latter is particularly important for morbidity control. In this review, the underlying assumptions used in a study mapping Schistosoma mansoni infection intensity in East Africa are examined. We argue that the assumption of stationarity needs to be relaxed, and that the negative binomial assumption might result in misleading inference because of a high number of excess zeros (individuals without an infection). We developed a Bayesian geostatistical zero-inflated (ZI) regression model that assumes a non-stationary spatial process. Our model is validated with a high-quality georeferenced database from western Côte d'Ivoire, consisting of demographic, environmental, parasitological and socio-economic data. Nearly 40% of the 3818 participating schoolchildren were infected with S. mansoni, and the mean egg count among infected children was 162 eggs per gram of stool (EPG), ranging between 24 and 6768 EPG. Compared to a negative binomial and ZI Poisson and negative binomial models, the Bayesian non-stationary ZI negative binomial model showed a better fit to the data. We conclude that geostatistical ZI models produce more accurate maps of helminth infection intensity than the spatial negative binomial ones.


1987 ◽  
Vol 17 (11) ◽  
pp. 1451-1454
Author(s):  
C. H. Meng ◽  
S. Z. Tang

The Canadian Pulp and Paper Association has defined the operational availability of a piece of logging equipment as A = (T − M − D)/T, where T denotes total scheduled machine hours per day, M denotes maintenance hours per day, and D denotes machine downtime per day. The existing literature on logging machines contains only point estimates of the mean operational availability. This paper propounds interval estimation as a preferable alternative since, unlike point estimation, it provides an indication of the uncertainty involved. Two methods of interval estimation are developed: (i) an analytical approach derived from basic theories and (ii) a Monte Carlo simulation. A detailed example is given to demonstrate the application of both methods to the same logging machine. For situations in which theoretical distributions for downtimes and repair times can be assumed, analytical solutions provide general and exact answers for the interval estimate of machine operational availability. However, if theoretical distributions cannot be reasonably assumed and if the integration involved is difficult, the analytical procedures become difficult. In such cases, operational availability can be approximated by the method of Monte Carlo simulation.


2006 ◽  
Vol 48 (1) ◽  
pp. 149-156 ◽  
Author(s):  
Lili Tian ◽  
Jianrong Wu

2006 ◽  
Vol 25 (12) ◽  
pp. 2125-2135 ◽  
Author(s):  
Jianrong Wu ◽  
A. C. M. Wong ◽  
Wei Wei

2013 ◽  
Vol 2 (4) ◽  
pp. 11
Author(s):  
NI MADE SEKARMINI ◽  
I KOMANG GDE SUKARSA ◽  
I GUSTI AYU MADE SRINADI

One method of regression analysis used to analyze the count data is Poisson regression. Poisson regression requires that the mean value equal to the value of variance (equidispersion). However, sometimes the data is going overdispersion  the state variance values ??greater than the mean value. One of the causes overdispersion is the excessive number of zero values ??on the response variable (excess zeros). One method of analysis that can be used on data that had overdispersion due to excess zeros is regression Zero-Inflated Negative Binomial (ZINB). The data that can be analyzed using the ZINB regression is the early childhood mortality in the province of Bali because much of the data is zero. The analysis showed that the data had overdispersion on Poisson regression, so the ZINB regression analysis was used. From the results of the ZINB regression can overcome overdispersion so it was better than the Poisson Regression Model.


2021 ◽  
Vol 50 (1) ◽  
pp. 59-73
Author(s):  
Young Eun Jeon ◽  
Suk-Bok Kang

We derive some estimators of the scale parameter of the Rayleigh distribution under the unified hybrid censoring scheme. We also derive some estimators of the reliability function and the entropy of the Rayleigh distribution. First, we obtain the maximum likelihood estimator of the scale parameter. Second, we obtain the Bayes estimator using the mean of the posterior distribution. Lastly, we obtain the Bayes estimator using the mode of the posterior distribution. We also derive the interval estimation (confidence interval, credible interval, and HPD credible interval) for the scale parameter under the unified hybrid censoring scheme. We compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. Coverage probability and average lengths of 95 % and 90% intervals are obtained.


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