Sneh Gulati

Parametric and nonparametric inference from record-breaking data

1. Introduction.- 2. Preliminaries and Early Work.- 3. Parametric Inference.- 4. Nonparametric Inference-Genesis.- 5. Smooth Function Estimation.- 6. Bayesian Models.- 7. Record Models with Trend.- References.

Smooth nonparametric estimation of thedistribution and density functions from record-breaking data

In some experiments, such as destructive stress testing and industrial quality control experiments, only values smaller than all previous ones are observed. Here, for such record-breaking data, kernel estimation of the cumulative distribution function and smooth density estimation is considered. For a single record-breaking sample, consistent estimation is not possible, and replication is required for global results. For m independent record-breaking samples, the proposed distribution function and density estimators are shown to be strongly consistent and asymptotically normal as m → ∞. Also, for small m, the mean squared errors and biases of the estimators and their smoothing parameters are investigated through computer simulations.

A web-based distributed system for hurricane occurrence projection

As an environmental phenomenon, hurricanes cause significant property damage and loss of life in coastal areas almost every year. Research concerning hurricanes and their aftermath is gaining more and more attention nowadays. This paper presents our work in designing and building a Web‐based distributed software system that can be used for the statistical analysis and projection of hurricane occurrences. Firstly, our system is a large‐scale system and can handle the huge amount of hurricane data and intensive computations in hurricane data analysis and projection. Secondly, it is a distributed system, which allows multiple users at different locations to access the system simultaneously and to share and exchange the data and data model. Thirdly, our system is a database‐centered system where the Oracle database is employed to store and manage the large amount of hurricane data, the hurricane model and the projection results. Finally, a three‐tier architecture has been adopted to make our system robust and resistant to the potential change in the lifetime of the system. This paper focuses on the three‐tier system architecture, describing the design and implementation of the components at each layer. Copyright

Goodness-of-Fit Statistics for the Exponential Distribution When the Data are Grouped

Abstract In many industrial and biological experiments, the recorded data consist of the number of observations falling in an interval. In this paper, we develop two test statistics to test whether the grouped observations come from an exponential distribution. Following the procedure of Damianou and Kemp (Damianou, C., Kemp, A. W. (1990). New goodness of statistics for discrete and continuous data. American Journal of Mathematical and Management Sciences 10:275–307.), Kolmogrov–Smirnov type statistics are developed with the maximum likelihood estimator of the scale parameter substituted for the true unknown scale. The asymptotic theory for both the statistics is studied and power studies carried out via simulations.

Smooth nonparametric estimation of the hazard and hazard rate functions from record-breaking data

Abstract Often in industrial quality control experiments and destructive stress testing, only values smaller than all previous ones are observed. Here, from such record-breaking data, nonparametric estimation of the hazard function and the hazard rate is considered. For a single record-breaking sample, consistent estimation is not possible except in the extreme tails of the distribution. Hence, replication is required and for m such independent record-breaking samples, strong consistency of the estimators is established as m → ∞. Also, the hazard function estimators are shown to be asymptotically normal. Finally, for small m, the mean squared errors and biases of the estimators are examined through computer simulations.

A reliable Web-based system for hurricane analysis and simulation

In this paper, we present our research and development efforts toward a reliable, large-scale, Web-based system for hurricane analysis and simulation. The major contributions of this system lie in the following three aspects: (1) it supports the multidisciplinary research efforts in predicting and simulating the hurricane damages and insured losses; (2) it is a large-scale, distributed, Web-based system, which allows both the professional and general users to conduct computational intensive on-line analysis simultaneously and to share and exchange the information; and (3) database management techniques are employed in our system to manage the huge amount of hurricane-related historical and simulated data.

SELECTING FAILURE MONITORING TIMES FOR AN EXPONENTIAL LIFE DISTRIBUTION

In certain situations in life testing, it is more practical to record whether a unit fails in an interval instead of measuring failure times exactly. This paper considers the analysis of life data from the exponential distribution with the use of period..

Kernel Density Estimation from Record-Breaking Data

In some experiments, only values smaller than all previous ones are observed, such as destructive stress testing and industrial quality control experiments. Here, for such record-breaking data, kernel density estimation is considered. For a single record-breaking sample, consistent estimation is not possible except in the extreme tails of the distribution. Hence, replication is required, and for m such independent record-breaking samples, the kernel density estimator is shown to be strongly consistent and asymptotically normal as m → ∞. Also, some computer simulation results and examples are presented.

Families of smooth confidence bands for the survival function under the general random censorship model

Randomly right censored data often arise in industrial life testing and clinical trials. Several authors have proposed asymptotic confidence bands for the survival function when data are randomly censored on the right. All of these bands are based on the empirical estimator of the survival function. In this paper, families of asymptotic (1-α)100% level confidence bands are developed from the smoothed estimate of the survival function under the general random censorship model. The new bands are compared to empirical bands, and it is shown that for small sample sizes, the smooth bands have a higher coverage probability than the empirical counterparts.

Goodness-of-Fit Tests for Pareto Distribution

The Pareto distribution can serve to model several types of datasets, especially those arising in the insurance industry. In this chapter, we present methods to test the hypothesis that the underlying data come from a Pareto distribution. The tests presented for both the type I and type II Pareto distributions are based on the regression test of Brain and Shapiro (1983) for the exponential distribution. Power comparisons of the tests are carried out via simulations.