Recent work has shown the important properties of the wind inversion residual or Maximum Likelihood Estimator (MLE) for Quality Control (QC) of QuikSCAT Hierarchichal Data Format (HDF) observations. Since March 2000, the QuikSCAT Near-Real Time (NRT) Binary Universal Format Representation (BUFR) product is available. As this product is used for Numerical Weather Prediction (NWP) assimilation pu...

The Kawasaki identity (KI) and the Jarzynski equality (JE) are important nonequilibrium relations. Both of these relations take the form of an ensemble average of an exponential function and can exhibit convergence problems when the average of the exponent differs greatly from the log of the average of the exponential function. In this work, we re-express these relations so that only selected r...

When dealing with a regular (fixed-support) one-parameter distribution, the corresponding maximum-likelihood estimator (MLE) is, to good approximation, normally distributed. But, when support boundaries are functions of parameter, finding approximation for sampling distribution MLE (needed construct an accurate confidence interval parameter’s true value) may get very challenging. We demonstrate...

Clock synchronization plays a crucial role in Wireless Sensor Networks (WSNs). Assuming that there is no clock skew between sensor nodes, the Maximum Likelihood Estimate (MLE) of clock offset was derived by [1] for clock synchronization protocols assuming exponential random delays and a two-way message exchange mechanism as in TPSN (Timing-sync Protocol for Sensor Networks [2]) or NTP (Network ...

This lecture covers the basics of core concepts in probability and statistics to be used in the course. These include random variables, continuous and discrete distributions, joint and conditional distributions, the chain rule, marginalization, Bayes Rule, independence and conditional independence, and expectation. Probability models are discussed along with the concepts of independently and id...

In this article, we proposed a new extension of the Topp–Leone family distributions. Some important properties model are developed, such as quantile function, stochastic ordering, series representation, moments, stress–strength reliability parameter, Renyi entropy, order statistics, and moment residual life. A particular member called extended exponential (NETLE) is discussed. Maximum likelihoo...

We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent α estimated from the data. We treat α as an unknown parameter, but for theoretical simplicity w...

Objective This paper presents an assessment of physical meanings of parameter and goodness of fit for homodyned K (HK) distribution modeling ultrasonic speckles from scatterer distributions with wide-varying spatial organizations. Methods A set of 3D scatterer phantoms based on gamma distributions is built to be implemented from the clustered to random to uniform scatterer distributions conti...

In this paper, we introduce a new continuous distribution mixing exponential and gamma distributions, called Sushila distribution. We derive some properties of the include: probability density function, cumulative expected value, moments about origin, coefficient variation (C.V.), skewness, kurtosis, moment generating reliability measures. The includes, special cases, as particular case p=1/2 (...

The Burr III distribution properly approximates many familiar distributions such as Normal, Lognormal, Gamma, Weibull, and Exponential distributions. It plays an important role in reliability engineering, statistical quality control, and risk analysis models. The Burr III distribution has four parameters known as location, scale, and two shape parameters. The estimation process of these paramet...