On confidence intervals for the mean past lifetime function under random censorship

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.

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Hacer estimaciones estadísticas

ENERO-JUNIO 2021 - Revista Innovaciones de Negocios ◽

10.29105/rinn5.10-10 ◽

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.

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

Frontiers in Digital Health ◽

10.3389/fdgth.2021.747460 ◽

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.

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Coverage versus Confidence

The Mathematica Journal ◽

10.3888/tmj.23-1 ◽

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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Improved approximate confidence intervals for the mean of a log-normal random variable

Statistics in Medicine ◽

10.1002/sim.1052 ◽

2002 ◽

Vol 21 (10) ◽

pp. 1443-1459 ◽

Cited By ~ 11

Author(s):

Douglas J. Taylor ◽

Lawrence L. Kupper ◽

Keith E. Muller

Keyword(s):

Confidence Intervals ◽

Random Variable ◽

Normal Random Variable ◽

The Mean ◽

Approximate Confidence Intervals ◽

Log Normal

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LINK OF MOMENTS BEFORE AND AFTER TRANSFORMATIONS, WITH AN APPLICATION TO RESAMPLING FROM FAT-TAILED DISTRIBUTIONS

Econometric Theory ◽

10.1017/s026646661800021x ◽

2018 ◽

Vol 35 (03) ◽

pp. 630-652 ◽

Cited By ~ 2

Author(s):

Karim M. Abadir ◽

Adriana Cornea-Madeira

Keyword(s):

Finite Number ◽

Confidence Intervals ◽

Characteristic Functions ◽

Infinite Variance ◽

Fundamental Relation ◽

Bootstrap Confidence Intervals ◽

Finite Samples ◽

Before And After ◽

The Mean ◽

Do So

Let x be a transformation of y, whose distribution is unknown. We derive an expansion formulating the expectations of x in terms of the expectations of y. Apart from the intrinsic interest in such a fundamental relation, our results can be applied to calculating E(x) by the low-order moments of a transformation which can be chosen to give a good approximation for E(x). To do so, we generalize the approach of bounding the terms in expansions of characteristic functions, and use our result to derive an explicit and accurate bound for the remainder when a finite number of terms is taken. We illustrate one of the implications of our method by providing accurate naive bootstrap confidence intervals for the mean of any fat-tailed distribution with an infinite variance, in which case currently available bootstrap methods are asymptotically invalid or unreliable in finite samples.

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Variability and Confidence Intervals for the Mean of Climate Data with Short- and Long-Range Dependence

Journal of Climate ◽

10.1175/jcli-d-17-0090.1 ◽

2018 ◽

Vol 31 (15) ◽

pp. 6135-6156 ◽

Cited By ~ 2

Author(s):

Matthew C. Bowers ◽

Wen-wen Tung

Keyword(s):

Confidence Intervals ◽

Long Range ◽

Long Memory ◽

Long Range Dependence ◽

Climate Data ◽

Temperature State ◽

Correlation Structures ◽

The Mean ◽

Error Bars ◽

Mean State

This paper presents an adaptive procedure for estimating the variability and determining error bars as confidence intervals for climate mean states by accounting for both short- and long-range dependence. While the prevailing methods for quantifying the variability of climate means account for short-range dependence, they ignore long memory, which is demonstrated to lead to underestimated variability and hence artificially narrow confidence intervals. To capture both short- and long-range correlation structures, climate data are modeled as fractionally integrated autoregressive moving-average processes. The preferred model can be selected adaptively via an information criterion and a diagnostic visualization, and the estimated variability of the climate mean state can be computed directly from the chosen model. The procedure was demonstrated by determining error bars for four 30-yr means of surface temperatures observed at Potsdam, Germany, from 1896 to 2015. These error bars are roughly twice the width as those obtained using prevailing methods, which disregard long memory, leading to a substantive reinterpretation of differences among mean states of this particular dataset. Despite their increased width, the new error bars still suggest that a significant increase occurred in the mean temperature state of Potsdam from the 1896–1925 period to the most recent period, 1986–2015. The new wider error bars, therefore, communicate greater uncertainty in the mean state yet present even stronger evidence of a significant temperature increase. These results corroborate a need for more meticulous consideration of the correlation structures of climate data—especially of their long-memory properties—in assessing the variability and determining confidence intervals for their mean states.

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