app7_mixtures_fin

app7_mixtures_fin - Application Example 7 DISTRIBUTION...

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Application Example 7 DISTRIBUTION MIXTURES One frequently deals with random variables the distribution of which depends on various factors. One example is the distribution of atmospheric parameters such as wind speed, barometric pressure, temperature, precipitation intensity etc. The distribution of these quantities varies with weather conditions and possibly time of the year. For example, wind speed has a very different distribution during inter-storm periods, in extratropical storms, and in tornadoes. Another example is the weight of vehicles on a highway. The distribution of the weight of a generic vehicle depends on the type of vehicle (say car, truck, or bike), as well as the day (weekend versus weekday) and hour of the day. The last two factors affect the mixture of vehicle types in a traffic stream. For example, in an urban area, the fraction of trucks is higher during the night than during the day. A third example is the strength of concrete, the distribution of which depends on the amount of water used in the mixture, the amount and type of aggregates and the curing conditions, among other factors. Let X be the variable of interest and denote by Θ a factor that influences the distribution of X. For simplicity, suppose that
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