, to determine the weighted mean of data, ni, drawn from a Poisson distribution, will, on average, underestimate the true mean by ∼1 for all true mean values larger than ∼3 when the common assumption is made that the error of the ith observation is σi = max( √ ni, 1). This small, but statistically significant offset, explains the long-known observation that chi-square minimization techniques wh...

I investigate the use of Pearson’s chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between theoretical models and low-count Poisson-distributed data. I demonstrate that these statistics should not be used to determine the goodness-of-fit with data...

According to the frequentists theory, it is assumed that unknown parameter θ is some xed number or vector. Given parameter value θ, we observe sample data X from distribution f(·|θ). To estimate parameter θ, we introduce an estimator T (X) which is a statistic, i.e. function of the data. This statistic is a random variable, since X. That is, the randomness here comes from randomness of sampling...

nowadays, hidden markov models are extensively utilized for modeling stochastic processes. these models help researchers establish and implement the desired theoretical foundations using markov algorithms such as forward one. however, using stability hypothesis and the mean statistic for determining the values of markov functions on unstable statistical data set has led to a significant reducti...

The use of PC cluster systems composed of many PCs is largely spread in these days. It is important to improve system usage keeping proper fair-share policy. Job scheduling is a function that dynamically allocates submitted jobs to hardware resource in user program execution units. This optimization problem is difficult to solve because many parameter are connected. In scheduler software, there...

2.1 Sufficient statistics. Classically, a " statistic " is a measurable function of the observations , say f (X 1 ,. .. , X n). The concept of " statistic " differs from that of " random variable " in that a random variable is defined on a probability space, so that one probability measure is singled out, where for statistics we have in mind a family of possible probability measures, R. A. Fish...

The two-parameter gamma model is widely used in reliability, environmental, medical and other areas of statistics. It has a two-dimensional sufficient statistic, and a two-dimensional parameter which can be taken to describe shape and mean. This makes it closely comparable to the normal model, but it differs substantially in that the exact distribution for the minimal sufficient statistic is no...

Often a question arises as to whether the observed data are a sample from a homogeneous population or the data have come from a heterogeneous population. In particular, one wants to test for a single normal distribution versus a mixture of two normal distributions. Classic asymptotic results fail to apply to the problem since the model does not satisfy the regularity conditions. This paper inve...

Inference about a parameter θ based on the likelihood function is often based on first order approximations to standard summary statistics from the likelihood, such as the likelihood ratio statistic or the standardized maximum likelihood estimate. For more accurate inference refinements are needed to both improve the first order approximation of the distribution of the relevant statistic, and t...