Raj S. Chhikara

The Inverse Gaussian Distribution as a Lifetime Model

Early occurrence of certain events such as failure or repairs is a common phenomenon in the lifetime of industrial products. Often, the log normal distribution has been found as a useful model to be applicable whenever the early occurrences dominate a lifetime distribution. In this paper we suggest the use of the inverse Gaussian distribution for a model of such lifetime behavior and discuss different reliability features of the distribution. It is shown that its failure rate is nonmonotonic, initially increasing and then decreasing. Advantages in the use of the inverse Gaussian over the log normal are given. Certain numerical results are presented for illustration.

Estimation of the Inverse Gaussian Distribution Function

Abstract Minimum variance unbiased estimates of the inverse Gaussian distribution function for all possible cases are given. A direct relationship is established between its density function and the normal density function, which throws more light on its salient features and possibly on its application in statistical inference. It is shown that the estimates are very similar in nature to those of the normal distribution and can be evaluated from the normal and Students t distribution tables.

Linear Discriminant Analysis With Misallocation in Training Samples

Abstract Linear discriminant analysis for a two-class case is studied in the presence of misallocation in training samples. A general approach to modeling of misallocation is formulated, and the mean vectors and covariance matrices of the mixture distributions are derived. The asymptotic distribution of the discriminant boundary is obtained, and the asymptotic first two moments of the error rates are given. Certain numerical results for the error rates are presented by considering the random and two nonrandom misallocation models.

Use of satellite spectral data in crop yield estimation surveys

Abstract Landsat Thematic Mapper data are utilized to improve upon the ground yield survey estimates for wheat in India. The normalized difference and ratio vegetation indices computed from the spectral responses are used to obtain homogeneous vegetation vigour stratifications of the cropland of the study area. Certain post-stratified estimators that make use of these stratifications are investigated and are shown to provide improved crop yield estimates.

Statistical distributions related to the inverse gaussian

Considering some useful functions of the inverse Gaussian variate we derive its related statistical distributions. in general, these distributions are shwn to have a certain anaogy vita several related distribution for the normal, and lead to inversting applicatons in developing sampling theory and statiatical inverse Gaussian.

Effect of mixed (boundary) pixels on crop proportion estimation

Abstract In estimating acreage proportions of crop types in a segment using Landsat data, considerable problem is caused by the presence of mixed pixels. Due to lack of understanding of their spectral characteristics, mixed pixels have been treated in the past as pure while clustering and classifying the segment data. This paper examines this approach of treating mixed pixels as pure pixels and the effect of mixed pixels on the bias and variance of a crop type proportion estimate. First, the spectral response of a boundary pixel is modeled and an analytical expression for the bias and variance of a proportion estimate is obtained. This is followed by a numerical illustration of the effect of mixed pixels on bias and variance. It is shown that as the size of the mixed pixel class increases in a segment, the variance increases; however, such increase does not always affect the bias of the proportion estimate.

Moderate increases in ambient PM2.5 and ozone are associated with lung function decreases in beach lifeguards.

Objective: Exposure to pollutants would adversely affect lung function of healthy athletes. Methods: Pulmonary function was recorded on beach lifeguards at three different times during the day. Daily and average peak pollutant levels were calculated. Linear regression analyses were made comparing lung function changes in response to pollutant levels. A multivariate model was constructed to explain the combined effects of pollutants. Results: Afternoon forced vital capacity (FVC) and forced expired volume in 1 second (FEV1) decreased significantly compared with morning values and decreased with increasing fine particulates (PM2.5). FEV1/FVC decreased with increasing ozone (O3) levels. Conclusion: The deleterious effect of PM2.5 and O3 were transient and occurred at pollutant levels far below national standards. At low levels of exposure, PM2.5 was associated with reduced lung volumes, while increasing O3 levels were associated with airway obstruction.

Optimum Test Procedures for the Mean of First Passage Time Distribution in Brownian Motion with Positive Drift (Inverse Gaussian Distribution)

In this paper we discuss testing hypotheses and interval estimation for the mean of the first passage time distribution in Brownian motion with positive drift (inverse Gaussian distribution). Optimum test procedures and confidence intervals for both one-sided and two-sided cases are derived in their exact forms, which utilize the percentage points of standard normal and Students t distributions. In thecase of an hypothesis with a two-sided alternative, it is shown that a uniformly most powerful (UMP) unbiased test is simply a two-tailed normal test if the nuisance parameter is known, and a two-tailed Students t test if it is unknown.

Crop Acreage Estimation Using a Landsat-Based Estimator as an Auxiliary Variable

The problem of improving upon the ground survey estimates of crop acreages by utilizing Landsat data is addressed. Three estimators, called regression, ratio, and stratified ratio, are studied. for bias and variance, and their relative efficiencies are compared. The approach is to formulate analytically the estimation problem that utilizes ground survey data, as collected by the U. S. Department of Agriculture ture, and Landsat data, which provide complete coverage for an area of interest, and then to conduct simulation studies. It is shown over a wide range of parametric conditions that the regression estimator is the most efficient unless there is a low correlation between the actual and estimated crop acreages in the sampled area segments, in which case the ratio and stratified ratio estimators are better. Furthermore, it is seen that the regression estimator is potentially biased due to estimating the regression coefficient from the training sample segments. Estimation of the variance of the regression estimator is also investigated. Two variance estimators are considered, the large sample variance estimator and an alternative estimator suggested by Cochran. The large sample estimate of variance is found to be biased and inferior to the Cochran estimate for small sample sizes.

Field size distributions for selected agricultural crops in the United States and Canada

Abstract Digitized agricultural field boundary data taken in the United States and Canada during the LACIE and AgRISTARS programs, in 1977 through 1980, were used to construct histograms showing the distributions of field area, width, and length for crops for which there were data for 700 or more fields per state. The observed distributions of area and width for fields of 10 crops grown in 13 states of the United States and Canada were compared with best-fit inverse Gaussian distributions and with log-normal distributions. For 28 distributions of area and 16 distributions of width there was found to be a probability of greater than .01 of their being inverse Gaussian. There were 10 distributions of area for which there was probability of greater than .005 of their being log-normal. Distributions of area and width stratified by state and crop type appear to be unique. The inverse Gaussian, which represents a wide range of statistical distributions from skewed to almost symmetrical, can provide a useful model for distributions of field area.