The Length-Biased Lognormal Distribution and Its Application in the Analysis of Data from Oil Field Exploration Studies

The length-biased version of the lognormal distribution and related estimation problems are considered and sized-biased data arising in the exploration of oil fields is analyzed. The properties of the estimators are studied using simulations and the use of sample mode as an estimate of the lognormal parameter is discussed

The Length-Biased Versus Random Sampling for the Binomial and Poisson Events

The equivalence between the length-biased and the random sampling on a non-negative, discrete random variable is established. The length-biased versions of the binomial and Poisson distributions are discussed

A Note on α-Curvature of the Manifolds of the Length-biased Lognormal and Gamma Distributions in View of Related Applications in Data Analysis

The α-curvature tensors of the statistical manifolds of the length-biased versions of the log-normal and gamma distributions are derived and discussed. This study was designed to investigate observations related to the parameter estimation for the length-biased lognormal distribution as a model for the lengthbiased data from oil field exploration

The Bootstrap Method for the Selection of a Shrinkage Factor in Two-stage Estimation of the Reliability Function of an Exponential Distribution

An application of a bootstrap method for selecting a suitable shrinkage factor for the two-stage shrinkage estimator of a reliability function for the exponential distribution is discussed. The estimator obtained here has higher efficiency as compared to the one where the shrinkage factor is not subjected to bootstrapping