Bounds for the mean of second largest order statistic in large samples

Statistics ◽  
1985 ◽  
Vol 16 (3) ◽  
pp. 457-464
Author(s):  
N. Balaxmshnan ◽  
P.C. Joshi
Keyword(s):  
Order Statistic ◽  
Large Samples ◽  
The Mean

The mean number of alleles in multigene families

1992 ◽  
Vol 24 (01) ◽  
pp. 1-19 ◽  
Author(s):  
G. A. Watterson
Keyword(s):  
Probability Distribution ◽  
Gene Conversion ◽  
Random Sample ◽  
Multigene Families ◽  
Explicit Formulas ◽  
Large Samples ◽  
The Mean

The paper considers a random sample of r chromosomes, each having n genes subject to intrachromosomal gene conversion, and mutation. The probability distribution and moments for the number of alleles present is investigated, when the number, k, of possible alleles at each locus, is either finite or infinite. Explicit formulas are given for the mean numbers of alleles on r = 1, 2, or 3 chromosomes, which simplify previously known results. For fixed r, in the infinitely-many-alleles case, the mean number increases asymptotically like r θ log (n) as n→∞, where θ is a mutation parameter. But results for large samples remain elusive.

The Oligocene rodent Ischyromys of the Great Plains: replacement mistaken for anagenesis

1993 ◽  
Vol 67 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Timothy H. Heaton
Keyword(s):  
South Dakota ◽  
Great Plains ◽  
Statistical Investigation ◽  
Closely Related Species ◽  
Geographic Ranges ◽  
Large Samples ◽  
Early Oligocene ◽  
Mean Size ◽  
The Mean ◽  
Entire Distribution

Ischyromys, the most abundant early Oligocene rodent from the Great Plains, has been considered by some workers to represent a single gradually evolving lineage comprising three or more chronospecies. Statistical investigation of large samples suggest instead that two closely related species coexisted, and the shift in mean size that was thought to represent anagenesis actually represents replacement. In Nebraska and eastern Wyoming both I. parvidens (small) and I. typus (large) were rare but of equal abundance in the Chadronian, I. parvidens was more prevalent in the early Orellan, and I. typus was more prevalent in the middle and late Orellan. In northeastern Colorado, northern South Dakota, and North Dakota I. typus is the only species of Ischyromys found in Orellan deposits, thus showing that the two species had differing geographic ranges.The mean size of I. typus does increase up section at all localities, but this change is minor and not deserving of chronospecies recognition. Much of this change occurred in the latest Orellan and earliest Whitneyan as I. typus approached extinction, and it was accomplished mostly by loss of small individuals rather than a shift of the entire distribution. Rate of evolutionary change in Ischyromys is found to be inversely correlated with population size, and no new species arose during the Orellan when Ischyromys was most abundant.

A probabilistic analogue of the mean value theorem and its applications to reliability theory

1999 ◽  
Vol 36 (3) ◽  
pp. 706-719 ◽  
Author(s):  
Antonio Di Crescenzo
Keyword(s):  
Steady State ◽  
Order Statistic ◽  
Arbitrary Order ◽  
Queueing Systems ◽  
Mean Value ◽  
Reliability Theory ◽  
Maintenance Cost ◽  
Mean Value Theorem ◽  
Probabilistic Generalization ◽  
The Mean

In a similar spirit to the probabilistic generalization of Taylor's theorem by Massey and Whitt [13], we give a probabilistic analogue of the mean value theorem. The latter is shown to be useful in various contexts of reliability theory. In particular, we provide various applications to the evaluation of the mean total profits of devices having random lifetimes, to the mean total-time-on-test at an arbitrary order statistic of a random sample of lifetimes, and to the mean maintenance cost for the second room of queueing systems in steady state characterized by two serial waiting rooms.

scholarly journals The Log-Linear Return Approximation, Bubbles, and Predictability

2012 ◽  
Vol 47 (3) ◽  
pp. 643-665 ◽  
Author(s):  
Tom Engsted ◽  
Thomas Q. Pedersen ◽  
Carsten Tanggaard
Keyword(s):  
Stock Returns ◽  
Upper Bound ◽  
Approximation Error ◽  
Expected Returns ◽  
Price Ratio ◽  
Rational Bubbles ◽  
Large Samples ◽  
Approximation Errors ◽  
The Mean ◽  
Log Linear

AbstractWe study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles that have explosive conditional expectation, and we investigate the magnitude of the approximation error in those cases. We find that, surprisingly, the Campbell-Shiller approximation is very accurate even in the presence of large explosive bubbles. Only in very large samples do we find evidence that bubbles generate large approximation errors. Finally, we show that a bubble model in which expected returns are constant can explain the predictability of stock returns from the dividend-price ratio that many previous studies have documented.

Approximating the Normal Sample Median Distribution in Process Control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Char Leung
Keyword(s):  
Process Control ◽  
Small Samples ◽  
Normal Sample ◽  
Normal Distribution Function ◽  
Engineering Process ◽  
Sample Median ◽  
Central Tendency Measure ◽  
Engineering Process Control ◽  
Large Samples ◽  
The Mean

Abstract The present work aims to propose an approximation of the sample median distribution with a normal parent distribution. Although the mean is usually used as the central tendency measure for normal samples, the median has also been used in engineering, process control in particular. The proposed method approximates the normal sample median distribution only using the normal distribution function. It outperforms Castagliola’s method for small samples and serves as an alternative approximation for trading off accuracy against computational complexity for large samples.

scholarly journals Why most experiments in psychology failed: sample sizes required for randomization to generate equivalent groups as a partial solution to the replication crisis

2017 ◽  
Author(s):  
Gjalt - Jorn Ygram Peters
Keyword(s):  
Confidence Interval ◽  
Scientific Method ◽  
Partial Solution ◽  
Evidence Base ◽  
Original Study ◽  
Sample Sizes ◽  
Large Samples ◽  
Replication Crisis ◽  
The Mean ◽  
Using Data

The experimental method is one of the staple methodological tools of the scientific method, and is as such prevalent in the psychological literature. It relies on the process of randomization to create equivalent groups. However, this procedure requires sufficiently large samples to succeed. In the current paper, we introduce tools that are based on the sampling distribution of Cohen’s d and that enable computing the likelihood that randomization succeeded in creating equivalent groups and the required sample size to achieve a desired likelihood of randomization success. The required sample sizes are considerable, and to illustrate this, we compute the likelihood of randomization failure using data from the Reproducability Project: Psychology. It is shown that it is likely that many original studies but also many replications failed to successfully create equivalent groups. For the replications, the mean likelihood of randomization failure was 44.54% (with a 95% confidence interval of [35.03%; 54.05%]) in the most liberal scenario, and 100% in the most conservative scenario. This means that many studies were in fact not experiments: the observed effects were at best conditional upon the value of unknown confounders, and at worst biased. In any case replication is unlikely when the randomization procedure failed to generate equivalent groups in either the original study or the replication. The consequence is that researchers in psychology, but also the funders of research in psychology, will have to get used to conducting considerably larger studies if they are to build a strong evidence base.

scholarly journals HUBUNGAN ANTARA JENIS PERSALINAN DENGAN KEBERHASILAN ASI EKSKLUSIF DI KECAMATAN BAKI KABUPATEN SUKOHARJO

2015 ◽  
Vol 3 (2) ◽  
Author(s):  
Warsini Warsini ◽  
Sri Aminingsih ◽  
Rizky Ayu Fahrunnisa
Keyword(s):  
Birth Weight ◽  
Exclusive Breastfeeding ◽  
Random Sampling ◽  
Maternal Age ◽  
Congenital Abnormalities ◽  
Normal Weight ◽  
Cross Sectional ◽  
Large Samples ◽  
The Mean ◽  
Cross Sectional Design

Background Results of Indonesia Demographic and Health Survey (IDHS) in 2012 showed coverage exclusive breastfeeding in Indonesia have not been optimal, that was 42 %. This study was conducted to analyze the correlation between the kinds of giving births with the success of exclusive breastfeeding 6 (six) months.The subject and Methods The study was a quantitative analytic observational cross-sectional design. Large samples are 100 mothers  who had babies aged 6-12 months. Sampling random sampling. Collecting data using questionnaires.The results showed that the average maternal age 20-35 years (80%), birth weight children mostly above 2,500 g (97%), maternal gestational age infants mostly pretty months (99%) and all infants the respondent was not born with congenital abnormalities, meaning that 100% of infants born with a normal weight difference, kinds of giving birth the mean of paravaginal (70%), the success rate of exclusive breastfeeding by 56%. Statistical shows that there is a positive correlation and statistically significant between the kinds of giving births with the success of exclusive breastfeeding (OR = 2.53 ; CI 95% 1.05 until 6.10 ; p = 0.035).Conclusion There was a significant correlation between the kinds of giving births with the success of exclusive breastfeeding.Keywords: the kinds of giving births, exclusive breastfeeding

scholarly journals Dental Caries Prevalence among 12–15 Year Old Palestinian Children

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Maen Mahfouz ◽  
Albina Abu Esaid
Keyword(s):  
Dental Caries ◽  
Clinical Examination ◽  
West Bank ◽  
Age Groups ◽  
Permanent Dentition ◽  
The Other ◽  
Caries Prevalence ◽  
Large Samples ◽  
The Mean ◽  
Palestinian Children

Objective. To measure the distribution of dental caries in a group of Palestinian adolescents. Material and Methods. A sample of 677 individuals of both sexes (411 were females and 266 were males) their ages ranged from 12 to 15 year old randomly selected from schools in northern west bank in Palestine. Clinical examination was performed on all the subjects focusing on the index DMFT, representing the number of teeth that were either decayed, missing or with extraction indicated, or restored. Results. The prevalence of dental caries in the permanent dentition was 54.35% and was the highest in 15 age 75.75% in comparison to the other ages (12, 13, and 14) (40.57%, 41.76%, and 60.47%), respectively. The mean DMFT for the sample was 5.39 ± 2.85525 while the mean DMFT for different age groups (12–15) was 5.52 ± 2.766, 5.58 ± 2.745, 5.23 ± 3.304, and 5.23 ± 2.606, respectively. The prevalence of dental caries was higher in females with DMFT 5.39 ± 2.854 than males with DMFT 5.26 ± 2.891. Conclusion. High prevalent dental caries was found among Palestinian adolescents and higher in females than males. Strict preventive programs should be implemented. Further research with large samples required to include all adolescents from Palestine.

scholarly journals Meta-analysis of rare binary events in treatment groups with unequal variability

2017 ◽  
Vol 28 (1) ◽  
pp. 263-274 ◽  
Author(s):  
Lie Li ◽  
Xinlei Wang
Keyword(s):  
Random Effects ◽  
Mean Squared Error ◽  
Meta Analysis ◽  
Random Effects Model ◽  
Treatment Groups ◽  
Continuity Correction ◽  
Large Samples ◽  
Squared Error ◽  
The Mean ◽  
Simple Average

Meta-analysis has been widely used to synthesize information from related studies to achieve reliable findings. However, in studies of rare events, the event counts are often low or even zero, and so standard meta-analysis methods such as fixed-effect models with continuity correction may cause substantial bias in estimation. Recently, Bhaumik et al. developed a simple average estimator for the overall treatment effect based on a random effects model. They proved that the simple average method with the continuity correction factor 0.5 (SA_0.5) is the least biased for large samples and showed via simulation that it has superior performance when compared with other commonly used estimators. However, the random effects models used in previous work are restrictive because they all assume that the variability in the treatment group is equal to or always greater than that in the control group. Under a general framework that explicitly allows treatment groups with unequal variability but assumes no direction, we prove that SA_0.5 is still the least biased for large samples. Meanwhile, to account for a trade-off between the bias and variance in estimation, we consider the mean squared error to assess estimation efficiency and show that SA_0.5 fails to minimize the mean squared error. Under a new random effects model that accommodates groups with unequal variability, we thoroughly compare the performance of various methods for both large and small samples via simulation and draw conclusions about when to use which method in terms of bias, mean squared error, type I error, and confidence interval coverage. A data example of rosiglitazone meta-analysis is used to provide further comparison.

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