On estimation of population mean based on two measurements

There are many estimators for population mean: arithmetic mean, median, root mean square, geometric mean, harmonic mean, and so forth. Which one is the best? Here, we answer this question given two measurements from a uniform distribution.     

Exact and approximate distributions for the product of inverted Dirichlet components

It is well known that X/(X+Y) has the beta distribution when X and Y follow the inverted Dirichlet distribution. In this paper, we derive the exact distribution of the product P=XY (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose two approximations and show evidence of their goodness of fit. The work is motivated by real-life examples.     

The true maximum-likelihood estimators for the generalized Gaussian distribution with p = 3, 4, 5

The generalized Gaussian distribution with location parameter μ, scale parameter σ, and shape parameter p contains the Laplace, normal, and uniform distributions as particular cases for p = 1, 2, +∞, respectively. Derivations of the true maximum-likelihood estimators of μ and σ for these special cases are popular exercises in many university courses. Here, we show how the true maximum-likelihood estimators of μ and σ can be derived for p = 3, 4, 5. The derivations involve solving of quadratic, cubic, and quartic equations.     

A new four-parameter lifetime distribution

Generalizing lifetime distributions is always precious for applied statisticians. In this paper, we introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley geometric (EPLG) distribution, obtained by compounding EPL and geometric distributions. The new distribution arises in a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters. It contains several lifetime distributions as particular cases: EPL, new generalized Lindley, generalized Lindley, power Lindley and Lindley geometric distributions. We derive several properties of the new distribution such as closed-form expressions for the density, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Simulation studies are also provided. Finally, two real data applications are given for showing the flexibility and potentiality of the new distribution.     

Between Decentralized Planning and Neo-liberalism: Challenges for the Survival of the Indigenous People of Kerala, India

This paper examines the experiences of decentralization under successive political regimes in Kerala in the context of neo‐liberal policies, with reference to the impact on the lives of adivasi (indigenous) communities. The Communist Party‐led government had been implementing a home‐grown programme of decentralized planning since 1996 until it lost power to the Congress Party‐led conservative coalition in 2001. In the context of the accelerated structural adjustment and liberalization of the national government, the new government amended its predecessor's programme with a reduced role for the state bureaucratic and political actors in mobilizing people for planning and implementing projects at the local level. Based on a comparative analysis, the authors argue that the new programme has so far not been successful as regards enabling marginalized groups such as the indigenous communities to resist exclusion and move out of their states of deprivation. The study also shows that the withdrawal of the state from the social and economic sectors has adversely affected these groups.     

Moments of some J-shaped distributions

This paper concerns a family of univariate distributions suggested by Topp & Leone in 1955. Topp & Leone provided no motivation for this new family and by way of properties they derived only the first four integer-order moments, i.e. E(Xn) for n=1, r 2, r 3, r 4 . In this paper we provide a motivation for the family of distributions and derive explicit algebraic expressions for: (1) hazard rate function; (2) E(Xn) when n ± 1 is any integer; (3) E(Xn) for n=1, r 2, r … r , r 10 , and (4) E[{X-E(X)} n] , n=2, r 3, r 4 . We also give an expression for the characteristic function and discuss issues on estimation and simulation. The main calculations of this paper use properties of the Gauss hypergeometric function.     

A unified method for constructing expectation tolerance intervals

Given a random sample of size \(n\) with mean \(\overline{X} \) and standard deviation \(s\) from a symmetric distribution \(F(x; \mu , \sigma ) = F_{0} (( x- \mu ) / \sigma ) \) with \(F_0\) known, and \(X \sim F(x;\; \mu , \sigma )\) independent of the sample, we show how to construct an expansion \( a_n^{\prime } = \sum _{i=0}^\infty \ c_i \ n^{-i} \) such that \(\overline{X} - s a_n^{\prime } < X < \overline{X} + s a_n^{\prime } \) with a given probability \(\beta \) . The practical value of this result is illustrated by simulation and using a real data set.     

Balakrishnan skew logistic distribution

Abstract

Based on Balakrishnan's (2002 Balakrishnan, N. (2002). Discussion on “Skew multivariate models related to hidden truncation and/or selective reporting” by B.C. Arnold and R.J. Beaver. Test 11: 37–39.[Web of Science ®] , [Google Scholar]) novel idea, a new skew logistic distribution is proposed. It contains Azzalini's skew logistic and standard logistic distributions as particular cases. Several mathematical properties of the proposed distribution (including characteristic function, cumulative distribution function, stochastic orderings, and simulation schemes) are derived. A real-data application is used to illustrate practical usefulness.     

Invariance principles and almost sure central limit theorem for the error variance estimator in linear models

A number of score statistics are derived for a heterogeneous spatial Poisson process which has a composite intensity. The intensity consists of a 'background' process which is estimated

from a control point process by kernel density estimation. The parametric form of the composite intensity yields score tests for particular spatial effects. A numerical example concerning respiratory cancer mortality is given.