Asian Journal of Probability and Statistics

This study was present a catastrophe put option pricing model that considers default risk. The default of the option issuer can occur at any time before the maturity, and there is a correlation between the total assets of the option issuer, the underlying stock and the zero coupon bond. The explicit solution of option pricing is obtained when the interest rate process follows the Vasicek model and relevant proofs are given. Finally, the value changes under different parameters are discussed through a numerical analysis.

The weighted distribution is mainly used in various real life fields such as ecology, reliability engineering, medical science etc. Some statistical properties are derived such as moment generating function, characteristic function, cumulative generating function, the hazard function, Renyi entropy, Cumulative residual entropy. For parameter estimation maximum likelihood estimation method is used. The considered weighted probability distribution is applied to two real data sets of waiting time to examine the suitability and applicability.

Aims: This study aimed to obtain the shape parameter of an Exponential Inverted Exponential distribution using different prior distributions under different loss functions.

Methodology: The Bayes’ theorem was adopted to obtain the posterior distribution of the shape parameter of an Exponential inverted Exponential distribution for both non-information prior (such as Jeffreys prior, Hartigen prior and Uniform prior) and an informative prior (such as Gamma distribution and chi-square distribution). Different loss functions (such as Entropy loss function, Square error loss function, Al-Bayyati’s loss function and Precautionary loss function) were employed to obtain the estimate parameter of the shape parameter with an assumption that the scale parameter is known.

Results: The posterior distribution of the shape parameter of an Exponential Inverted Exponential distribution follows a Gamma distribution for all the prior distribution in the study. Also the Bayes estimate for the simulated datasets and real life dataset were obtained.

Conclusion: The Bayes’ estimates for different prior distribution under different loss functions are close to the true parameter value of the shape parameter. The estimators are then compared in terms of their Mean Square Error (MSE) which is computed using R programming language. We deduce that the MSE reduces as the sample size (n) increases.

In this paper, we compared different Parameter Estimation method of the two parameter Weibull-Rayleigh Distribution (W-RD) namely; Maximum Likelihood Estimation (MLE), Least Square Estimation method (LSE) and three methods of Quartile Estimators. Two of the quartile methods have been applied in literature, while the third method (Q1-M) is introduced in this work. The methods have been applied to simulate data. These methods of estimation were compared using Error, Mean Square Error and Total Deviation (TD) which is also known as Sum Absolute Error Estimate (SAEE). The analytical results show that the performances of all the parameter estimation methods were satisfactory with data set of Weibull-Rayleigh distribution while degree of accuracy is determined by the sample size. The proposed quartile (Q1-M) method has the least Total Deviation and MSE. In addition, the quartile methods perform better than MLE for the simulated data. In particular, the proposed quartile methods (Q1-M) have an added advantage of simplicity in usage than MLE methods.

The study focussed on the empirical examination of, food, beverage, accommodation sectors, cleanliness and hygiene of the destinations to meet the satisfaction of the tourists. Our study confirmed that around 94% of the respondents would like to visit Kashmir again and around 98% of the respondents would recommend this destination (Kashmir) to their friends. Moreover, maximum percentage of the respondents (around 80%), agreed that Indian media is playing negative role regarding the Kashmir issue and more than the same percentage of the respondents (around 82%), agreed that Kashmir is a safer place than anywhere else for visiting. Tourism is the life line of the Kashmir valley and hence all possible efforts need to be undertaken for retaining, maintaining and sustaining it.