On estimating the scale parameter of the exponential distribution with a known linear relation between the location and the scale parameter

In this article we study the estimation of the average excess life θ in a two-parameter exponential distribution with a known linear relationship between α (the minimum life) and θ of the form α = aθ, where a is known and positive. A comparison of the efficiencies of estimators which are linear combinations of the smallest sample value and the sample sum of deviations from the smallest sample value and the maximum likelihood estimators is made for various sample sizes and different values of a. It is shown that these estimators are dominated in the risk by the minimum-risk scale equivariant estimator based on sufficient statistics. A class of Bayes estimators for inverted gamma priors is constructed and shown to include a minimum-risk scale equivariant estimator in it. All the members of this class can be computed easily.     

On the moments of gamma order statistics

A recurrence relation between the moments of order statistics from the gamma distribution having an integer parameter r is obtained. It is shown that if the negative moments of orders -(r?1), …, ?1 of the smallest order statistic in random samples of size n are known, then one can obtain all the moments. Tables of negative moments for r = 2 (1) 5 are also given.     

India's Military Instrument: A Doctrine Stillborn

For six years, India has sought to implement an army doctrine for limited war, ‘Cold Start’, intended to enable a Cold War era force optimised for massive offensives to operate under the nuclear threshold. This article asks whether that is presently feasible, and answers in the negative. Doctrinal change has floundered on five sets of obstacles, many of which are politically rooted and deep-seated, thereby leaving the Army unprepared to respond to challenges in the manner envisioned by the doctrine's architects.     

Product moments of order statistics from the doubly truncated exponential distribution

Recurrence relations for the product moments of order statistics from a doubly truncated exponential distribution are obtained. These relations allow us to evaluate the product moments for all sample sizes.     

Samudra: India’s convoluted path to undersea nuclear weapons

ABSTRACT

India is advancing slowly toward operationalizing its nuclear triad. Its first nuclear-propelled ballistic-missile submarine (SSBN), the INS Arihant, conducted its maiden deterrent patrol in November 2018. However, doubts exist around the capability of India’s SSBN, the effectiveness of its command and control, and its effects on regional stability in South Asia. This article examines the history and future trajectory of India’s sea-based nuclear forces and describes how India seeks to maintain robust command and control over its undersea nuclear weapons.