scholarly journals The Shortest Confidence Interval for the Mean of a Normal Distribution

2018 ◽  
Vol 7 (2) ◽  
pp. 33
Author(s):  
Traoré Boubakar ◽  
Diabaté Lassina ◽  
Touré Belco ◽  
Fané Abdou
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Mathematical Statistics ◽  
Standard Normal Distribution ◽  
Pivotal Quantity ◽  
Construction Technique ◽  
Standard Normal ◽  
The Mean ◽  
Shortest Confidence Intervals

An interesting topic in mathematical statistics is that of the construction of the confidence intervals. Two kinds of intervals which are both based on the method of pivotal quantity are the shortest confidence interval and the equal tail confidence intervals. The aim of this paper is to clarify and comment on the finding of such intervals and to investigation the relation between the two kinds of intervals. In particular, we will give a construction technique of the shortest confidence intervals for the mean of the standard normal distribution. Examples illustrating the use of this technique are given.

Constructing a confidence interval for the ratio of normal distribution quantiles

2020 ◽  
Vol 26 (4) ◽  
pp. 325-334
Author(s):  
Ahad Malekzadeh ◽  
Seyed Mahdi Mahmoudi
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Pivotal Quantity ◽  
Simple Method ◽  
Normal Populations ◽  
Generalized Pivotal Quantity ◽  
Variance Estimate

AbstractIn this paper, to construct a confidence interval (general and shortest) for quantiles of normal distribution in one population, we present a pivotal quantity that has non-central t distribution. In the case of two independent normal populations, we propose a confidence interval for the ratio of quantiles based on the generalized pivotal quantity, and we introduce a simple method for extracting its percentiles, based on which a shorter confidence interval can be created. Also, we provide general and shorter confidence intervals using the method of variance estimate recovery. The performance of five proposed methods will be examined by using simulation and examples.

scholarly journals COMPARACION DEL PROMEDIO Y LA MEDIANA COMO ESTIMADORES DE LA MEDIA PARA MUESTRAS NORMALES DEPENDIENDO DEL TAMAÑO DE MUESTRA

2017 ◽  
Vol 23 (2) ◽  
pp. 33
Author(s):  
José W. Camero Jiménez ◽  
Jahaziel G. Ponce Sánchez
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Hypothesis Tests ◽  
Sample Mean ◽  
Palabras Clave ◽  
The Mean ◽  
The Difference

Actualmente los métodos para estimar la media son los basados en el intervalo de confianza del promedio o media muestral. Este trabajo pretende ayudar a escoger el estimador (promedio o mediana) a usar dependiendo del tamaño de muestra. Para esto se han generado, vía simulación en excel, muestras con distribución normal y sus intervalos de confianza para ambos estimadores, y mediante pruebas de hipótesis para la diferencia de proporciones se demostrará que método es mejor dependiendo del tamaño de muestra. Palabras clave.-Tamaño de muestra, Intervalo de confianza, Promedio, Mediana. ABSTRACTCurrently the methods for estimating the mean are those based on the confidence interval of the average or sample mean. This paper aims to help you choose the estimator (average or median) to use depending on the sample size. For this we have generated, via simulation in EXCEL, samples with normal distribution and confidence intervals for both estimators, and by hypothesis tests for the difference of proportions show that method is better depending on the sample size. Keywords.-Sampling size, Confidence interval, Average, Median.

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 A New Linear Regression Kalman Filter with Symmetric Samples

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2139
Author(s):  
Xiuqiong Chen ◽  
Jiayi Kang ◽  
Mina Teicher ◽  
Stephen S.-T. Yau
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Particle Filter ◽  
Normal Distribution ◽  
Extended Kalman Filter ◽  
Nonlinear Filtering ◽  
Unscented Kalman Filter ◽  
Standard Normal Distribution ◽  
Leibler Divergence ◽  
Standard Normal

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

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.

The computation of standard normal distribution integral in any required precision based on reliability method

2018 ◽  
Vol 48 (6) ◽  
pp. 1517-1528
Author(s):  
Yuge Dong ◽  
Haimeng Zhang ◽  
Liangguo He ◽  
Can Wang ◽  
Minghui Wang
Keyword(s):  
Normal Distribution ◽  
Standard Normal Distribution ◽  
Reliability Method ◽  
Standard Normal
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