Li and Shaked (2007) introduced the family of generalized total time on test transform (TTT) stochastic orders, which is parameterized by a real function h that can be used to capture the preferences of a decision maker. It is natural to look for properties of these orders when there is an uncertainty in determining the appropriate function h. In this paper we study these orders when h is nondecreasing. We note that all these orders are location independent, and we characterize the dispersive order, and the location-independent riskier order, by means of the generalized TTT orders with nondecreasing h. Further properties, which strengthen known properties of the dispersive order, are given. A useful nontrivial closure property of the generalized TTT orders with nondecreasing h is obtained. Applications in poverty comparisons, risk management, and reliability theory are described.

We determined the after-tax income required to finance basic needs for Canadian elders living with different circumstances in terms of age, gender, city of residence, household size, homeowner or renter status, means of transportation, and health status. Using 2001 as our base year, we priced the typical expenses for food, shelter, medical, transportation, miscellaneous basic living items and home-based long-term care for elders living in five Canadian cities. This is the first Canadian study of basic living expenses tailored to elders instead of adults in general, prepared on an absolute rather than a relative basis. We also accounted for an individual’s unique life circumstances and established the varying effect that they have on the cost of basic expenses, particularly for home care. We found that the maximum Guaranteed Income Supplement and Old Age Security benefit did not meet the cost of basic needs for an elder living in poor circumstances.