Ulhas Jayram Dixit

Estimation of parameters of the gamma distribution in the presence of outliers

The maximum likelihood estimators and moment estimators are derived for samples from the Gamma distribution in the presence of outliers. These estimators are compared empirically when all the three parameters are unknown and when one of the three parameters is known; their bias and mean square error (MSE) are investigated with the help of numerical technique.

Efficient Estimation of the Parameters of the Pareto Distribution in the Presence of Outliers

The moment(MM) and least squares(LS) estimations of the parameters are derived for the Pareto distribution in the presence of outliers. Further, we have derived a mixture method(MIX) of estimations with MM and LS that shows that the MIX is more efficient. In the final section we have given an example of actual data from a medical insurance company.

Bayesian approach to prediction in the presence of outliers for Weibull distribution

The predictive distribution of ther-th order statistics is obtained for the future sample based on the original sample from Weibull distribution in the presence ofk outliers. Next, in the presence ofk outliers two sample case is considered where prediction can be on ther2-th order statistics in the second sample based on ther1-th order statistics in the first sample. Finally, extension top-sample case is made for a particular case of predicting minimum in thep-th sample based on minimum in earlier samples. An illustration is provided with simulated samples where minimum is actually predicted in one and two sample cases.

On the estimation of the power of the scale parameter of the gamma distribution in the presence of outliers

The estimation of power of the scale parameter (σ) is derived for samples from the gamma distribution in the presence of k outliers by using a generalized loss function. Here, estimators of the type hTrare considered for σr, where T is a real valued random variable whose distribution depends on an unknown real parameter σ. We have obtained the Bayes estimate of (∞,σ) under various priors for the same loss function in the presence of k outliers.

Testing of the Parameters of a Right Truncated Exponential Distribution

SYNOPTIC ABSTRACT Here we obtain optimum tests of hypotheses about the parameters c(truncation point) and θ (scale parameter) of a Right Truncated Exponential Distribution (RTED).

Bound for the Variance

The history of the lower bounds on the variance of the estimators is long and has many contributors.

Most Powerful Test

Suppose that your parliament is considering a proposal for uniform civil code for all religions. To gather information, a group surveys 500 randomly selected individuals from their district and learns that 65 % of these people favor the proposal.

Sufficiency and Completeness

Suppose that a random variable (rv) X is known to have a Gamma distribution \(G(p,\sigma )\) but we do not know one of the parameters, say, \(\sigma \).

Bayesian inference for the Pareto lifetime model in the presence of outliers under progressive censoring with binomial removals

Here we have used Type II progressive censoring with random removal for the Pareto lifetime model in the presence of outliers. The number of units removed at each failure time follows a Binomial distribution. The analysis is based on Bayesian approach. In the last, we have given examples with real data.

Estimation of the Scale Parameter of the Exponential Distribution in the Presence of Outliers Using Linex Loss Function

SYNOPTIC ABSTRACT The estimation of the scale parameter θ is derived for samples from the exponential distribution in the presence of outliers by using linex loss function. The risk function of the estimator is derived and compared with that of an admissible estimator relative to linex loss function. It is shown that estimator based on linex loss function is better in some region. Examples of failures in microcirculation & weight indicator housings are given in the end.