1. Nonparametric Estimation of the Limiting Interval Reliability for Stationary Dependent Sequences

    Angel Mathew1, N. Balakrishna2

    1. Department Statistics, Maharaja’s College, Ernakulam, 682011, Kerala, India.
    2. Department Statistics, Cochin University of Science and Technology, Cochin, 682022, Kerala, India

    Abstract: In this paper, we consider the nonparametric estimation of the limiting interval reliability of a repairable system when the sequences of failure and repair times are generated by stationary dependent sequence of random variables. The proposed nonparametric estimator is shown to be consistent and asymptotically normal. A simulation study is also conducted to assess the performance of the proposed estimator using a first-order exponential autoregressive process.

    Keywords: limiting interval reliability, availability, repairable systems, exponential autoregressive process.

    Pages: 45 – 53 | Full PDF Paper
  2. Second Order Bias Corrected Efficient GMM Estimator

    B F Chakalabbi, Sagar Matur and Sanmati Neregal

    Department of Statistics, Karnatak University’s Karnatak Arts College, Dharwad – 580001, India

    Abstract: In this paper, the three conventional GMM estimators First-difference, Level and System GMM estimators with respective efficient initial weight matrices are considered to estimate the autoregressive panel data model. It is observed that the bias of first-difference GMM estimator is heigher and the bias of system GMM estimator is lesser among the above mentioned estimators but as variance ratio in-creases and as autoregressive parameter approaches to one the bias of all the afore-mentioned estimators increase. Hence to reduce such bias, second order bias correction method is considered. Through Monte-Carlo simulation it is observed that the considered second order bias correction method works well for first-difference and system GMM estimators, specially when the variance ratio is greater than one.

    Keywords: First-difference GMM estimator, Level GMM estimator, System GMM estimator, Second order bias.

    Pages: 54 – 75 | Full PDF Paper
  3. Fuzzy Almost p*-Compact Space

    Anjana Bhattacharyya

    Department of Mathematics, Victoria Institution (College), 78 B, A.P.C. Road, Kolkata – 700009, India.

    Abstract: In [1], fuzzy p*-open set is introduced and studied. Using this concept as a basic tool, in this paper a new type of fuzzy compactness, viz., fuzzy almost p*-compactness is introduced. Afterwards, this concept is characterized especially by fuzzy net and prefilterbase. In the last section, it is shown that fuzzy almost p*-compact space is fuzzy almost compact [3] and the converse is true in fuzzy p*-regular space [1]. Lastly it is proved that fuzzy almost p*-compactness remains invariant under fuzzy almost p*-continuous function [1].

    Keywords: Fuzzy p*-open cover, fuzzy regularly p*-closed set, fuzzy almost p*-compact set (space), p*-adhere point of a prefilterbase, p*-cluster point of a fuzzy net.

    Pages: 76 – 88 | Full PDF Paper
  4. Pointwise Gauge Field and Relativistic Structure

    Wang Yiping

    Zhejiang Quzhou Association of Senior Scientists and Technicians Zhejiang Quzhou 324000.

    China • Qianjiang Mathematics and Power Engineering Institute Zhejiang Quzhou 324000.

    Abstract: The quantization element concept of which infinite pointwise is mechanics element and space-time geometry possesses random “asymmetry and nonuniformity” and other factors is proposed; combination of gauge field and relativistic structure (circle logarithm) is proposed, which includes gravitational field, electromagnetic field, nuclear field, thermodynamic field and photon field to constitute pointwise quantum eleven-dimensional space and the first and second gauge invariance and build relativistic structure (circle logarithm), realizing “exact solution within [0-1/2-1] [0~1/2~1] under the topological variation rule without specific contents”. It is provided with a superiority of conciseness, self-consistency and zero error, and is widely applicable to physics, astronomy and mechanics fields.

    Keywords: Gauge field Pointwise quantization General relativity Relativistic structure (circle logarithm)  Limit topological phase transition

    Pages: 89 – 98 | Full PDF Paper