正如@sascha的注解所述，从日期到时间值的转换完成了这项工作：

#!/usr/bin/env python3

import time
import numpy

_DATE_RANGE = ('1925-01-01', '1992-01-01')
_DATE_FORMAT = '%Y-%m-%d'
_EMPIRICAL_SCALE_RATIO = 0.15
_DISTRIBUTION_SIZE = 1000

def main():
    time_range = tuple(time.mktime(time.strptime(d, _DATE_FORMAT))
                       for d in _DATE_RANGE)
    distribution = numpy.random.normal(
        loc=(time_range[0] + time_range[1]) * 0.5,
        scale=(time_range[1] - time_range[0]) * _EMPIRICAL_SCALE_RATIO,
        size=_DISTRIBUTION_SIZE
    )
    date_range = tuple(time.strftime(_DATE_FORMAT, time.localtime(t))
                       for t in numpy.sort(distribution))
    print(date_range)

if __name__ == '__main__':
    main()

请注意，您可以（应该？）使用scipy.stats.truncnorm来生成truncated normal distribution，而不是_EMPIRICAL_SCALE_RATIO。

这里是一个使用datetime模块的实现，它还允许生成小时、分钟、秒，并使用Numpy/Pandas友好的日期格式。

from datetime import datetime
import numpy

def main(start, end, date_format,  distribution_size, scale_ratio):
    # Converting to timestamp
    start = datetime.strptime(start, date_format).timestamp()
    end = datetime.strptime(end, date_format).timestamp()
    
    # Generate Normal Distribution
    mu = datetime.strptime('1958-01-01T00:00:00', date_format).timestamp()
    sigma = (end - start) * scale_ratio
    total_distribution = np.random.normal(loc=mu, scale=sigma,  size=distribution_size)
    
    # Sort and Convert back to datetime
    sorted_distribution = numpy.sort(total_distribution)
    date_range = tuple(datetime.fromtimestamp(t) for t in sorted_distribution)
    print(date_range)


start = '1925-01-01T00:00:00'
end = '1992-01-01T00:00:00'
date_format = '%Y-%m-%dT%H:%M:%S'

main(start=start, end=end, date_format=date_format, distribution_size=1000, scale_ratio=0.05)

结果：

您也可以混合多个分布，如下所示：

dist_1 = np.random.normal(loc=mu_1, scale=sigma_1,  size=size_1)
dist_2 = np.random.normal(loc=mu_2, scale=sigma_2,  size=size_2)
all_distributions = np.concatenate([dist_1, dist_2])