Construction of Confidence Intervals for the Mean of a Population Containing Many Zero Values

1998 ◽  
Vol 16 (3) ◽  
pp. 362 ◽  
Author(s):  
Alan H. Kvanli ◽  
Yaung Kaung Shen ◽  
Lih Yuan Deng
Keyword(s):  
Confidence Intervals ◽  
Zero Values ◽  
The Mean

scholarly journals A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 679
Author(s):  
Jimmy Reyes ◽  
Emilio Gómez-Déniz ◽  
Héctor W. Gómez ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
New Family ◽  
Tail Distribution ◽  
Zero Values ◽  
The Mean ◽  
Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

scholarly journals Assessment of decrease in renal function associated with hypothyroidism

2021 ◽  
Vol 12 (1) ◽  
pp. 275-286
Author(s):  
Ayesha Ammar ◽  
Kahkashan Bashir Mir ◽  
Sadaf Batool ◽  
Noreen Marwat ◽  
Maryam Saeed ◽  
...  
Keyword(s):  
Renal Function ◽  
Confidence Interval ◽  
Creatinine Clearance ◽  
Confidence Intervals ◽  
Standard Error ◽  
Radioactive Iodine ◽  
T Test ◽  
Euthyroid State ◽  
Significant Difference ◽  
The Mean

Objective: Study was aimed to see the effects of hypothyroidism on GFR as a renal function. Material and methods: Total of Fifty-eight patients were included in the study. Out of those forty-eight patients were female and the rest were male. Out of fifty eight patients, fifty three patients were of thyroid cancer in which hypothyroidism was due to discontinuation of thyroxine before the administration of radioactive iodine for Differentiated thyroid cancer.Moreover, remaining five patients were post radioactive iodine treatment (for hyperthyroidism) hypothyroid. All of the patients were above eighteen years of age with TSH value > 30µIU/ml. Pregnant and lactating females were excluded.Renal function tests (urea/creatinine, creatinine clearance) and serum electrolytes followed by Tc-99m-DTPA renal scan for GFR assessment (GATES’ method) were carried out in all subjects twice during the study, One study during hypothyroid state (TSH > 30 µIU/ml) and other during euthyroid state (TSH between 0.4 to 4µ IU/ml). The results of Student’s t-test showed significant difference in renal functions (Urea, creatinine, creatinine clearance, GFR values) in euthyroid state and hypothyroid state (p-value <0.05). RESULTS: In case of creatinine the paired t test reveal the mean 1.014±0.428, with standard error of 0.669 within 95% confidence interval, for creatinine clearance 80.11±14.12 with standard error of 1.94 within 95% confidence intervals, for urea the mean 28±12.13 with standard error of 1.607 within 95% confidence intervals and for GFR for individual kidney is 38.056±8.56 with standard error of 1.3717 within 95% confidence interval. There was no difference in the outcome of the 2 groups. Conclusion: Hypothyroidism impairs renal function to a significant level and hence needs to be prevented and corrected as early as possible.

scholarly journals Hacer estimaciones estadísticas

2017 ◽  
Vol 5 (10) ◽  
Author(s):  
M. H Badii
Keyword(s):  
Confidence Intervals ◽  
Statistical Estimation ◽  
Good Estimator ◽  
The Mean ◽  
The Difference

Keywords: Estimations, sampling, statisticsAbstract. The notion of statistical estimation both in terms of point and interval is described. The criteria of a good estimator are noted. The procedures to calculate the intervals for the mean, proportions and the difference among two means as well as the confidence intervals for the probable errors in statistics are provided.Palabras clave: Estadística, estimación, muestreoResumen. En la presente investigación se describen la noción de la estimación estadística, tanto de tipo puntual con de forma de intervalo. Se presentan los criterios que debe reunir un estimador bueno. Se notan con ejemplos, la forma de calcular la estimación del intervalo para la media, la proporción y de la diferencia entre dos medias y los intervalos de confianza para los errores probables.

scholarly journals Accurate Estimation of Heart and Respiration Rates Based on an Optical Fiber Sensor Using Adaptive Regulations and Statistical Classifications Spectrum Analysis

2021 ◽  
Vol 3 ◽  
Author(s):  
Rongjian Zhao ◽  
Lidong Du ◽  
Zhan Zhao ◽  
Xianxiang Chen ◽  
Jie Sun ◽  
...  
Keyword(s):  
Heart Rate ◽  
Individual Differences ◽  
Optical Fiber ◽  
Confidence Intervals ◽  
Respiration Rate ◽  
Spectrum Analysis ◽  
Optical Fiber Sensor ◽  
Fiber Sensor ◽  
Respiration Rates ◽  
The Mean

The aim of this work is to present a method for accurately estimating heart and respiration rates under different actual conditions based on a mattress which was integrated with an optical fiber sensor. During the estimation, a ballistocardiogram (BCG) signal, which was obtained from the optical fiber sensor, was used for extracting the heart rate and the respiration rate. However, due to the detrimental effects of the differential detector, self-interference, and variation of installation status of the sensor, the ballistocardiogram (BCG) signal was difficult to detect. In order to resolve the potential concerns of individual differences and body interferences, adaptive regulations and statistical classifications spectrum analysis were used in this paper. Experiments were carried out to quantify heart and respiration rates of healthy volunteers under different breathing and posture conditions. From the experimental results, it could be concluded that (1) the heart rates of 40–150 beats per minute (bpm) and respiration rates of 10–20 breaths per minute (bpm) were measured for individual differences; (2) for the same individuals under four different posture contacts, the mean errors of heart rates were separately 1.60 ± 0.98 bpm, 1.94 ± 0.83 bpm, 1.24 ± 0.59 bpm, and 1.06 ± 0.62 bpm, in contrast, the mean errors of the polar beat device were 1.09 ± 0.96 bpm, 1.44 ± 0.99 bpm, and 1.78 ± 0.94 bpm. Furthermore, the experimental results were validated by conventional counterparts which used skin-contacting electrodes as their measurements. It was reported that the heart rate was 0.26 ± 2.80 bpm in 95% confidence intervals (± 1.96SD) in comparison with Philips sure-signs VM6 medical monitor, and the respiration rate was 0.41 ± 1.49 bpm in 95% confidence intervals (± 1.96SD) in comparison with ECG-derived respiratory (EDR) measurements for respiration rates. It was indicated that the developed system using adaptive regulations and statistical classifications spectrum analysis performed better and could easily be used under complex environments.

scholarly journals Coverage versus Confidence

2021 ◽  
Vol 23 ◽  
Author(s):  
Peyton Cook
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Coverage Probability ◽  
Negative Binomial ◽  
Asymptotic Confidence Interval ◽  
Population Proportion ◽  
Coverage Probabilities ◽  
The Mean

This article is intended to help students understand the concept of a coverage probability involving confidence intervals. Mathematica is used as a language for describing an algorithm to compute the coverage probability for a simple confidence interval based on the binomial distribution. Then, higher-level functions are used to compute probabilities of expressions in order to obtain coverage probabilities. Several examples are presented: two confidence intervals for a population proportion based on the binomial distribution, an asymptotic confidence interval for the mean of the Poisson distribution, and an asymptotic confidence interval for a population proportion based on the negative binomial distribution.

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